From the diagram, ABCD is a rectangle. The equation of line BC is given by 3y+x=25. Given that the area of rectangle ABCD is 80 units². Find the coordinates of the points B, C and D.​ Point A(-1,2).​

Answer:

$52.96

Step-by-step explanation:

To find the total cost of his clothing, add up the prices of everything he bought.

Jeans: $23.00

Shirt: $14

Ties: 2 ties for $7.98 each.

Each tie costs $7.98, and the man bought two ties. Therefore, multiply 2 and $7.98

2*$7.98 = $15.96

Add all the prices together.

jeans + shirt + ties

$23 + $14 + $15.96

$37 + $15.96

$52.96

The total cost of his clothing is $52.96

Answer:

total cost=52.96

Step-by-step explanation:

Things he bought:

jeans for $23.00

a shirt for $14.00

two ties for $7.98 each

the total const would be the sum of all his clothes

which is

jeans for $23.00

+shirt for $14.00

+one tie for $7.98

+one tie for $7.98

_______________

total cost=52.96

HOPE IT HELPS :0

PLEASE MARK IT THE BRAINLIEST!

Step-by-step explanation:

firstly suppose f(X) as y and later interchange it with x and solve it to get inverse function of x.

The inverse of the given function is [tex]f^{-1}(x)=\dfrac{x+4}{2}[/tex].

Important information:

We need to find the inverse of the given function.

Substitute [tex]f(x)=y[/tex].

[tex]y=2x-4[/tex]

Interchange [tex]x[/tex] and [tex]y[/tex].

[tex]x=2y-4[/tex]

Isolate [tex]y[/tex].

[tex]x+4=2y[/tex]

[tex]\dfrac{x+4}{2}=y[/tex]

Substitute [tex]y=f^{-1}(x)[/tex].

[tex]\dfrac{x+4}{2}=f^{-1}(x)[/tex]

Thus, the inverse of the given function is [tex]f^{-1}(x)=\dfrac{x+4}{2}[/tex].

Find out more about 'Inverse of a function' here:

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Answer:

11/100 or 0.11

Step-by-step explanation:

10^-2 is also equal to 1/100

10^-1 is also equal to 1/10

Simply add them now:

1/100+1/10

= 1/100+ 10/100

= 11/100=0.11

Hope this helped!

Answer:

y = 9x

Step-by-step explanation:

First find the slope

m = (y2-y1)/(x2-x1)

    = (0-9)/(0-1)

   -9/-1

   9

The y intercept is 0 since the y value is 0 when x=0

The slope intercept form is y = mx+b where m is the slope and b is the y intercept

y = 9x +0

y = 9x

Answer:

(B) {(2,1),(4,3),(5,7)}

Step-by-step explanation:

If the same x value goes to 2 different y values, it is not a function

(A) {(2,3),(2,5),(4,7)}   the x value 2 goes to 3 and 5

(B) {(2,1),(4,3),(5,7)}

(C) {(3,-2),(2,4),(3,6)}  3 goes to -2 and 6

(D) {(-1,4),(-1,5),(2,5)}​-1 goes to 4 and 5

Answer:

it's the step by step proceedure you use when solving an equation. Parentethese (do this first)

Exponents (take care of that after parentheses)  

Multiplication

Division

Addition

subtraction (always the last step in the problem)

Step-by-step explanation:

Answer:

PEMDAS = ( ), Exponents, Multiplication, Division, Addition, Subtraction

Step-by-step explanation:

essentially, PEMDAS are an order of a rule in which you have to follow.

1. P = Parenthesis/ ( )

2. E= Exponents/ ²

3. M= Multiplication/ x

4. D= Division/ ÷

5. A= Addition/+

6. S= Subtraction/-

Each goes in order, and if there isn't one of the steps included in the math problem you are given, then its better to move on to the next uwu

I hope this was helpful owo

Answer:

when a number is divisible by 9, then the number is divisible by 3.

Step-by-step explanation:

They tell us "When a number is divisible by 9, the number is divisible by 3" we could change it by:

when a number is divisible by 9, then the number is divisible by 3.

Which makes sense because the number 9 is a multiple of the number 3, which means that the 9 can be divided by 3, therefore, if the number can be divided by 9, in the same way it can be divided by 3 .

Answer:

a

Step-by-step explanation:

Answer:

a) 0.2218 to 0.7057

b) 0.4710 to 0.8401

Step-by-step explanation:

Given:

sample = n = 18

sample variance = s² = 0.36

To find:

a) 90% confidence interval estimate of the population variance.

b) 90% confidence interval estimate of the population standard deviation.

a)

Compute degree of freedom

degree of freedom = df = n - 1 = 18 - 1 = 17

Compute value of α for a 90% confidence interval  

The confidence level for 90% is:

c = 0.90

So

α = 1 - c = 1 - 0.90 = 0.1

α = 0.1

Now use the table of critical values of the chi-square distribution in order to find critical values. Search for the 17th row of table using df = 17 and find the column corresponding to 1 - α/2 i.e. 0.95 of table for upper tail critical values and column corresponding to α /2 i.e. 0.05 of table for lower tail critical values.

Using the table:

[tex]X^{2}_{0.95}[/tex] = 8.672

[tex]X^{2}_{0.05}[/tex] = 27.587

90% Confidence interval estimate of the population variance

The boundaries of CI are computed using formula:

(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex]  ≤ σ² ≤ (n−1) s² / [tex]X^{2}_{1-\alpha/2}[/tex]

(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex]  = (18-1) 0.36 / 27.587

                       = (17) 0.36 / 27.587

                       =  6.12 / 27.587

(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex]  = 0.2218

(n−1) s² / [tex]X^{2}_{1-\alpha/2}[/tex] = (18-1) 0.36 / 8.672

                          = (17) 0.36 / 8.672

                          =  6.12 / 8.672

                          = 0.7057

This results in inequalities 0.2218 ≤ σ² ≤ 0.7057 for the variance

b)

90% Confidence interval estimate of the population standard deviation

The boundaries of CI are computed using formula:

√(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex]  ≤ σ ≤ √(n−1) s² / [tex]X^{2}_{1-\alpha/2}[/tex]

√(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex]  = √((18-1) 0.36 / 27.587)

                          = √((17) 0.36 / 27.587)

                          =  √(6.12 / 27.587)

                          = √0.2218

                          = 0.4709

                          = 0.4710

√(n−1) s² / [tex]X^{2}_{1-\alpha/2}[/tex] = √((18-1) 0.36 / 8.672)

                            = √((17) 0.36 / 8.672)

                            = √ (6.12 / 8.672)

                            = √0.7057

                            = 0.8401

0.4710 ≤ σ ≤ 0.8401 for the standard deviation.

Answer:

Step-by-step explanation:

Hello,

[tex]x = (fof^{-1})(x)=f(f^{-1}(x))=\dfrac{-2}{f^{-1}(x)}-1\\\\<=>f^{-1}(x)(x+1)=-2\\\\<=> f^{-1}(x)=\dfrac{-2}{x+1}[/tex]

and this is g(x)

so they are inverses

Hope this helps

Answer:

9/14

Step-by-step explanation:

3/7 + 50%×3/7 =

= 3/7 + 1/2×3/7

= 3/7 + 3/14

= 6/14 + 3/14

= 9/14

The required fraction which 50% grater than 3/7 is 9/14.

Fraction to determine that 50% grater than 3/7.

Fraction of the values is number represent in form of Numerator and denominator.

Here, fraction = 50% grater than 3/7
                     = 1.5 x 3/7
                    = 4.5/7
                     =  45/70
                     = 9/14

Thus, The required fraction which 50% grater than 3/7 is 9/14.

Learn more about fraction here:
https://brainly.com/question/10354322

#SPJ5

Answer:

The answer is -24√35

Step-by-step explanation:

-6√7 × 4√5

Using the rules of surds multiply the numbers outside the square root and the ones inside

That's

(-6×4)(√ 7 × √5)

= - 24√7×5

= -24√35

Hope this helps you

Answer:

-24√35

Step-by-step explanation:

-6√7 × 4√5

-6 × √7 × 4 √5

-6 × 4 × √7 × √5

-24 × √(7 × 5)

-24√35

Answer:

6 ± i and 6 ± i

Step-by-step explanation:

Let x be the first number.

Let y be the second number.

x + y = 12

x × y = 37

Solve for x in the first equation.

x = 12 - y

Put x as 12-y in the second equation and solve for y.

(12- y)y = 37

12y - y² = 37

- y² + 12y - 37 = 0

y = 6 ± i

Put y as 6 ± i in the first equation and solve for x.

x + 6 ± i = 12

x = 12 - 6 ± i

x = 6 ± i

Answer:

Option B - 0.02

Step-by-step explanation:

In this question, the p-value is used to tell us the probability that a difference of (0.88 – 0.68) which is 0.2 or greater would occur in the distribution of simulated differences. This is created done with the assumption that there is no true difference in the two populations.

Due to the fact that the researchers found the difference in proportions to be statistically significant, hence these results would rarely occur due to just the sampling variability and thus the p-value must be small.

Looking at the options, the p-value in Option (B) will be the correct response,l as it indicates that a difference of 0.2 or more would only occur about 2% of the time by chance alone provided the proportion who text were the same in the population of seniors and the population of freshmen. This resonates well with the claim that the difference in proportions is statistically significant.

Thus, Option B is the correct answer.

Answer:

12 m

Step-by-step explanation:

Given that the design, ABCD, was dilated to get a photocopy, EFGH, a scale factor or ratio was multiplied by the original lengths of the design to get the new measurement of the photocopy.

Thus, we are given the ratio, CD:GH = 2:3.

This means, any of the corresponding lengths of both figures would be in that same ratio.

Using the ratio of the design to the photocopy, 2:3, we can find the length of side EH of the photocopy.

The corresponding side of EH in the design is AD = 8m. Thus, AD to EH = ⅔

[tex] \frac{AD}{EH} = \frac{2}{3} [/tex]

[tex] \frac{8}{EH} = \frac{2}{3} [/tex]

Cross multiply

[tex] 3*8 = 2*EH [/tex]

[tex] 24 = 2*EH [/tex]

Divide both sides by 2 to make EH the subject of formula

[tex] \frac{24}{2} = \frac{2*EH}{2} [/tex]

[tex] 12 = EH [/tex]

The length of side EH = 12 m

Answer:

D. 0° to 90°

Step-by-step explanation:

If we see curve of sin(o) on coordinate,  we will notice that value of sin curve increases from 0 to 90 degrees and then decreases from 90 to 180 degrees.

Hence option D is correct.

Alternatively

we see that

sin 0 = 0

sin 30 = 1/2

sin 45 = 1/[tex]\sqrt{2}[/tex]

sin 60 = [tex]\sqrt{3} /2[/tex]

sin 90 = 1

Thus, we see  that value of sin is increasing from 0 to 90

now lets see value of sin from 90 to 180

sin 90 = 1

sin 120 = [tex]\sqrt{3} /2[/tex]

sin 135 = 1/[tex]\sqrt{2}[/tex]

sin 150 = 1/2

sin 180 = 0

Thus, we see  that value of sin is decreasing from 90 to 180.

Answer:

40

Step-by-step explanation:

P(Hugo is on time for a given class)=71%=0.71

If there are 57 classes during the semester

The number of times Hugo is on time to class during the semester will

=0.71 X 57

=40.47

[tex]\approx 40 $ (correct to the nearest integer.)[/tex]

Hugo is on time to class approximately 40 out of 57 times.

Answer:

9.2 ounce bottle cost $6.12 is better buy with unit price of $0.22

Step-by-step explanation:

Unit price of any product is given by

unit price = weight of product/ price of product

Given sizes

A

13.5 ounces bottle cost $2.98

cost of 1 ounce of shampoo for this size = cost price/weight of shampoo

 cost of 1 ounce of shampoo for this size =2.98/13.5 = $0.22

Unit price for this size is $.022

B

9.2 ounce bottle cost $6.12

cost of 1 ounce of shampoo for this size = cost price/weight of shampoo

 cost of 1 ounce of shampoo for this size =6.12/9.2 = 0.66

Unit price for this size is $0.66

As $0.22 is less than $0.66 thus,

9.2 ounce bottle cost $6.12 is better buy.

Answer:

x+10=1/2*(x+2)

2x+20=x+2

20-2= x-2x

x= -18

now,

LN= X+10

= -18+10

= -8

Answer:      x<2   or   xϵ(-∞; 2)

Step-by-step explanation:

Add +3.2x to both sides of inequality:

2.5-1.2x+3.2x<6.5-3.2x+3.2x

2.5+2x<6.5

Deduct 2.5 from both sides of inequality:

2.5-2.5+2x<6.5-2.5

2x<4

Divide both sides of inequality by 2

2x/2<4/2

x<2   or   xϵ(-∞; 2) ( the answer can be written in 2 ways)

Answer:

2.5 - 1.2x < 6.5 - 3.2x

add 3.2x to both sides;

2.5 + 2x < 6.5

minus 2.5 from both sides;

2x < 4

 x < 2

Step-by-step explanation:

This is the exact same as doing a linear equation, so brush up on this skill.

Answer: I had the same assingment and came here looking for answers myself. When I saw the only anwser was 20 (Which is wrong) I decided I would try my best and If I got it right come back here and share the correct answers for future students.

Just look at the PDF attached below, I somehow got a 50/50.

Step-by-step explanation:

Statements                                                   Reasons

1. △EGC ≅ △EGB                                     1. Given

2. EB ≅ EC                                              Supposition

3. <EGC ≅ <EGB                                       Given

4. Equilateral  Triangle                       EB ≅ EC ≅ BC

5. Equilateral  Triangle                      m∠BEC = 60°

Statements                                                 Reasons

1. △BEC is equilateral                      AAS≅AAS postulate (angle angle side)

2. m∠ GCE = 60°                                   m∠ BEC = 60°  Equilateral Triangles

3. FG ⊥ BC &  FG ⊥ AD                                   ABCD is a square

4.  m∠ECD +  m∠ BEC = 30°+60°                           Substitution (right angles)

m∠DCG = 90°                                                  right angles of a square

m∠BED=   135°

Statements                                                   Reasons

1. △ECG ≅ △EBG                                             Given

2.  ABCD is a square                                       Given

3. BC ≅ BE                                                     Given

4. AB ≅ DC                                                   ABCD is a square

5.  m∠ABE ≅  m∠DCE                           Outside angles of congruent  

                                                               triangles △EGB≅      △EGC    

5.  △AEB≅ △DEC                         S.S.A ≅ S.S.A. ( side side angle) Postulate

△BEC is equilateral                                m∠BEC = 60°

△ECD is isosceles                                 m CD= mCE

∠ECD = 30°                                          m∠BEC = 60°

As m∠BEC +∠ECD = 30°+ 60°          right angle of the square ABCD

The equal sides of the isosceles triangles are called the legs and the unequal third side is called the base.

Angles opposite to the equal sides of the isosceles triangle must also be equal.

As the third angle is 30° so the other two angles must be 75° each to make a total of 180°.

m∠BED=  m∠BEC +  m∠CED

             = 60° + 75°= 135°

https://brainly.com/question/22140109

Answer:

B. 17°.

Step-by-step explanation:

To solve the problem, we can use SOH CAH TOA.

SOH = Sine, Opposite divided by Hypotenuse

CAH = Cosine, Adjacent divided by Hypotenuse

TOA = Tangent, Opposite divided by Hypotenuse

In this case, we are given both the opposite and the hypotenuse, so we will use sine to solve it.

sine(N) = 4 / 14

sine(N) = 2 / 7

N = sec(2/7)

N = 16.6015496, which is about B. 17°.

Hope this helps!

Answer:

[tex]-\frac{10}{3}ft/s[/tex]

Step-by-step explanation:

We are given that

Height of man=5 foot

[tex]\frac{dy}{dt}=-10ft/s[/tex]

Height of street light=20ft

We have to find the rate of change of the length of his shadow when he is 25 ft form the street light.

ABE and CDE are similar triangle because all right triangles are similar.

[tex]\frac{20}{5}=\frac{x+y}{x}[/tex]

[tex]4=\frac{x+y}{x}[/tex]

[tex]4x=x+y[/tex]

[tex]4x-x=y[/tex]

[tex]3x=y[/tex]

[tex]3\frac{dx}{dt}=\frac{dy}{dt}[/tex]

[tex]\frac{dx}{dt}=\frac{1}{3}(-10)=-\frac{10}{3}ft/s=-\frac{10}{3}ft/s[/tex]

Hence, the rate of change of the length of his shadow when he is 25 ft from the street light=[tex]-\frac{10}{3}ft/s[/tex]

Answer:

Step-by-step explanation:

First, we need to divide the amount into 2 equal parts:

$819/2 = $414.50

Now, because they spent $183 more on textbooks, we add half of that to $414.50.

$414.50 + $91.50 = $506

$414.50 - $91.50 = $323

To make sure that the amount spent on textbooks is $183 more than the amount spent on course materials and computers, we need to add $183 to $323. If we get $506, our answer is correct.

$323 + $183 = $506 ✅

Answer:

Step-by-step explanation:

Let the cost of washer be ' x '

Let the cost of dryer be ' y '

According to Question,

x + y = 744 -----> equation (i)

x - y = 94 ------> equation (ii)

Adding equation (i) and (ii),

x + y = 744

+ x - y = 94

---------------------

2x = 838

Dividing both sides of the equation by 2

2x/2 = 838/2

Calculate

X = 419

Again,

Putting the value of X in equation (i)

X + y = 744

419 + y = 744

subtract 419 on both sides

y + 419 - 419 = 744 - 419

Calculate:

y = 325

The cost of dryer is $ 325.

Hope this helps...

Good luck on your assignment...

Answer: 107.67°C

Step-by-step explanation:

I guess that we could do a Taylor expansion around the point (2, 1)

Remember that a Taylor expansion around the point (a, b) is:

[tex]T(x,y) = T(a, b) + \frac{dT(a,b)}{dx}(x - a) + \frac{dT(a,b)}{dy}(y - b) + .....[/tex]

Where the latter terms need higher orders of the derivates of T, so we can not find them, regardless of that, this expansion will be accurate near the point (a, b),

Then, using this, we can write our expanssion as:

T(x,y) = 107 + 9*(x - 2) - 8*(y - 1)

Now we evaluate this in x = 2.03 and y = 0.95

T(2.03, 0.95) =  107 + 9(2.03 - 2) - 8*(0.95 - 1) = 107.67

Then a good estimation of the temperature at the point (2.03,0.95) is 107.67°C

The estimate of the temperature of the unevenly heated metal plate at temperature at the point (2.03,0.95) is;

T(2.03, 0.95) = 107.67 °C

Formula for taylor expansion around a point (a, b) is given as;

T(x, y) = T(a,b) +  [tex]\frac{dT(a,b)}{dx}[/tex](x - a) +  [tex]\frac{dT(a,b)}{dy}[/tex](y - b) + ....

We are given;

T(2,1) = 107

T'x(2,1) = [tex]\frac{dT(a,b)}{dx}[/tex] = 9

T'y(2,1) = [tex]\frac{dT(a,b)}{dy}[/tex] = −8

Plugging in the relevant values into our taylor expansion above gives;

T(x, y) = 107 + 9(x - 2) - 8(y - 1)

Now, we want to estimate the temperature at the point (2.03, 0.95).

Thus, we will plug in x = 2.03 and y = 0.95 to get;

T(2.03, 0.95) = 107 + 9(2.03 - 2) - 8(0.95 - 1)

T(2.03, 0.95) = 107 + 0.27 + 0.4

T(2.03, 0.95) = 107.67 °C

Read more at; https://brainly.com/question/9211177

Answer:

a) The sample space for this experiment includes

(Clubs, head), (Clubs, tail), (spades, head), (spades, tail), (diamonds, head), (diamonds, tail), (hearts, head), (hearts, tail)

b) The two events are not mutually exclusive or disjoint as both events can occur at the same time and the set of A intersect B is not an empty set and P(A n B) ≠ 0.

c) P(A u B) = (3/4) = 0.75

d) P(A n B') = (1/4) = 0.25

Step-by-step explanation:

Let A be the event a club or spade is picked from a regular 52-card deck.

Let B the event a heads appears when the coin is tossed.

a) A sample space consists of all the possible outcomes of the whole process of picking a random suit and then tossing the coin for heads or tails.

There are 4 suits in a 52 deck card namely, clubs, spades, diamonds and hearts.

And in a toss of a coin, there are only 2 possible outcomes, a head or a tail.

The possible outcomes for the random pick of cards include

{clubs, spades, diamonds, hearts}

And for the second event

{Head, tail}

Combined, the sample space is

(Clubs, head), (Clubs, tail), (spades, head), (spades, tail), (diamonds, head), (diamonds, tail), (hearts, head), (hearts, tail)

Noting that P(A) = probability of a club or a spade being picked = (26/52) = (1/2)

P(A') = Probability that a club or spade will not be picked, that is, a diamond or a heart will be picked = (26/52) = (1/2)

P(B) = Probability of a head turning up from the coin toss = (1/2)

P(B') = Probability of a head not turning up, that is, a tail turning up = (1/2)

b) Disjoint events are events that are mutually exclusive and cannot both occur at the same time. The set of the intersection of the two mutually exclusive/disjoint events is a null set.

Mathematically, mutually exclusive/disjoint events are proven through the relation that P(A n B) = 0.

But from the sample spaces obtained in (a) above, the event

(A n B) = (Clubs, head), (spades, head)

And it isn't a null set.

Since the probability of an event is the number of elements in the event divided by the total number of elements in the sample space.

n(A n B) = 2

n(total sample space) = 8

P(A n B) = (2/8) = (1/4) ≠ 0

Hence, the two events aren't disjoint.

c) P(A u B)

This represents the probability of obtaining a club or spade from the deck of card or getting head from the coin toss.

From the Total sample space, the set (A u B) includes (Clubs, head), (Clubs, tail), (spades, head), (spades, tail), (diamonds, head), (hearts, head)

n(A u B) = 6

n(total sample space) = 8

P(A u B) = (6/8) = (3/4) = 0.75

d) P(A n B')

This represents the probability of obtaining a club or spade from the deck of card and NOT getting a head from the coin toss.

The set (A n B') includes (Clubs, tail), (spades, tail)

n(A n B') = 2

n(total sample space) = 8

P(A n B') = (2/8) = (1/4) = 0.25

Hope this Helps!!!

Answer:

A) Option B is correct.

H₀: μ₁ = μ₂

Hₐ: μ₁ - μ₂ < 0

B) t = -2.502

p-value = 0.0112

C) Option A is correct.

Reject H₀. The data suggests that cola has a higher average compression strength than the strawberry drink.

D) Option A is correct.

The distributions of compression strengths are approximately normal.

Step-by-step explanation:

The complete Question is presented in the two attached images to this answer.

A) To perform this test we first define the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, we want to test if the extra carbonation of cola results in a higher average compression strength. That is, that cola has a higher average compression strength than the strawberry drink.

Hence, the null hypothesis would be that there isn't significant evidence to suggest that the extra carbonation of cola results in a higher average compression strength, that is, cola has a higher average compression strength than the strawberry drink.

The alternative hypothesis is that there is significant evidence to suggest that the extra carbonation of cola results in a higher average compression strength, that is, cola has a higher average compression strength than the strawberry drink.

Mathematically, if the average compression strength of strawberry drink is μ₁, the average compression strength of cola is μ₂ and the difference in compression strengths is μ = μ₁ - μ₂

The null hypothesis is represented as

H₀: μ = 0 or μ₁ = μ₂

The alternative hypothesis is represented as

Hₐ: μ < 0 or μ₁ - μ₂ < 0

B) So, to perform this test, we need to compute the test statistic

Test statistic for 2 sample mean data is given as

Test statistic = (μ₁ - μ₂))/σ

σ = √[(s₂²/n₂) + (s₁²/n₁)]

μ₁ = average compression strength of strawberry drink = 537

n₁ = sample size of the sample of strawberry drink in cans surveyed = 10

s₁ = standard deviation of the compression strength of strawberry drink in cans surveyed= 22

μ₂ = average compression strength of cola = 559

n₂ = sample size of the sample of cola in cans surveyed = 10

s₂ = standard deviation of the compression strength of strawberry drink in cans surveyed = 17

σ = [(17²/10) + (22²/10)] = 77.5903160379 = 8.792

We will use the t-distribution as no information on population standard deviation is provided

t = (537 - 559) ÷ 8.792

= -2.502 = -2.50

checking the tables for the p-value of this t-statistic

Degree of freedom = df = n₁ + n₂ - 2 = 10 + 10- 2 = 18

Significance level = 0.05

The hypothesis test uses a one-tailed condition because we're testing in only one direction (whether compression strength of cola in can is greater).

p-value (for t = -2.50, at 0.05 significance level, df = 18, with a one tailed condition) = 0.011154 = 0.0112 to 4 d.p.

C) The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.0112

0.0112 < 0.05

Hence,

p-value < significance level

This means that we reject the null hypothesis accept the alternative hypothesis & say that the extra carbonation of cola results in a higher average compression strength, that is, cola has a higher average compression strength than the strawberry drink.

D) The necessary conditions required before a t-test is deemed valid include.

- The samples used must be a random sample of the population distribution with each variable in the sample independent of other one.

- The distribution of the population where the samples were extracted from must be normal or approximately normal to ensure some degree of normality for the samples.

Hence, the necessary assumption for this t-test among the options is that the distributions of compression strengths are approximately normal.

Hope this Helps!!!

Answer: 585 miles

Step-by-step explanation: 60 x 7 for the first 7 hours = 420 miles, then 3 x 55 for the last 3 hours = 165 add them together, 420+265 you get= 585

60 miles per hour x 7 hours = 420 miles

55 miles per hour x 3 hours = 165 miles

Total miles = 420 + 165 = 585 miles

Answer:

1. what is a residual?

A. A residual is a value of y -y, which is the difference between an observed value of y and a predicted value of y.

2. The regression line has the property that the_sum of squares_of the residuals is the minimum possible sum.

Step-by-step explanation:

1. What is a​ residual?

A. A residual is a value of y -y, which is the difference between an observed value of y and a predicted value of y.

2. In what sense is the regression line the straight line that​ "best" fits the points in a​ scatterplot?

The regression line has the property that the_sum of squares_of the residuals is the minimum possible sum.

A residual is a value {Δy} that is a difference between an observed value of {y} and a predicted value of {y}.  

A regression line is an estimate of the line that describes the true, but unknown, linear relationship between the two variables. Mathematically -

[tex]$Y_i=f(X_i, \beta)+e_i[/tex]

Given is residual.

The residual for each observation is the difference between predicted values of y (dependent variable) and observed values of y. Mathematically -

[tex]r = x-x_{0}[/tex]

Therefore, a residual is a value {Δy} that is a difference between an observed value of {y} and a predicted value of {y}.  

To solve more questions on regression line, visit the link below -

https://brainly.com/question/7656407

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Answer: (10 - 3) x 25 = 175

Step-by-step explanation:

10 - 3 = 7

            7 x 25 = 175