Match each correlation coefficient, r, to its description.
r = −0.08
r = −0.83
r = 0.96
r = 0.06

1.) strong negative correlation
2.) weak positive correlation
3.) weak negative correlation
4.) strong positive correlation

Answer:

9π or 28.3 units²

Step-by-step explanation:

A = πr²

A = π(3)²

A = 9π

or

A= 28.3 units²

Hope this helps. :)

Answer:

3rd Matrix

Step-by-step explanation:

When you start putting the coefficients in as the matrix, you see that -9 has to be the 1st number, so that eliminates choice B and choice D as answers. You are left with choices A and C. C is the correct choice because when you plug in the second equation, your coefficient is -5, not 0.

Answer:

First Matrix

Step-by-step explanation:

Looking at the first equation, we see that the leading coefficient is -9. This gets rid of choice B and D because the first number in these matrices are not -9. You are left with choices A and C. Looking at the second equation, we see that there is no "w" variable, so we need to add one. The coefficient of this "w" is going to be 0. This means that A is the correct choice. Just to be sure though, evaluate all other coefficients to see if they line up with the matrix. Hope this helps.

Step-by-step explanation:

It is not specified the compounding period, which in general is a month these days.  So we will assume money is compounded each month, otherwise there is no point depositing monthly.

1. Yolanda:

APR=5% is equivalent to

Monthly interest = 5%/12 = 5/12% = 5/1200 = 1/240 = i

Monthly deposit = 100 = A

Future value after 14 years = 14*12 months = 168 months = n

FV1 =  A((1+i)^n-1)/i

=100*((1+1/240)^168-1)/(1/240)

= $24259.83

2. Zach

He deposits 1200 at the end of the year.  The last payment does not benefit from interest.

Since it is a yearly payment, each amount earns interest over a year, giving an annual interest of

(1+i)^12 -1 = 1.051161897881733 -1 =0.051161897881733 = j

Thus for 13 annual payments with annual interest j gives a compounded amount after 14 years, plus the last payment which does not earn interest

FV2 = A((1+j)^n-1)/j

= 1200((1.051161897881733)^13-1)/(0.051161897881733)+1200

= 22613.34

Summary

Total investments:

Yolanda = 12*100*14 = 16800

Zach = 1200 * 14 = 16800

So both investors have invested $16800 over the 14 year period.

Since Yolanda achieves a higher future value after 14 years ($24259.83) over that of Zach ($22613.34), financially Yolanda has a better strategy.

Note:

If zach had invested annually at the beginning of the year, he would have obtained:

A((1+j)^n-1)/j

= 1200((1.051161897881733)^14-1)/(0.051161897881733)

= 24908.88

which is superior over Yolanda's return.

Answer: 1/35

Step-by-step explanation:

1/5 = 0.2

0.2/7= 1/35

Answer:

Step by step explanation

[tex] \frac{1}{5} \div 7[/tex]

Dividing is equivalent to multiplying with the reciprocal:

[tex] \frac{1}{5} \times \frac{1}{7} [/tex]

Multiply the fraction

[tex] \frac{1 \times 1}{5 \times 7} [/tex]

[tex] = \frac{1}{35} [/tex]

Hope this helps...

Good luck on your assignment.

Answer:

The required sample size increases.

Step-by-step explanation:

The margin of error of a confidence interval is given by:

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which z is related to the confidence level(the higher the confidence level the higher z), [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

In this question:

The confidence level decreases, so z decreases.

For the margin of error to stay the same, the sample size also has to decrease.

The required sample size increases.

━━━━━━━☆☆━━━━━━━

▹ Answer

#3. 1.89/100

▹ Step-by-Step Explanation

1.89 → hundreths place so..

1.89/100 is the correct answer

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

3x

Step-by-step explanation:

If Dan is x years old and Olly is 3 times as old, that means that Olly's age is 3 * x or 3x for short.

Answer:

3x

Step-by-step explanation:

If Dan is x years old and Olly is 3 times old as Dan, then the expression is 3x.

Answer:

-72

Step-by-step explanation:

3*24=72

So he is 72 foot below see level or -72

Martin descended to a depth of 72 feet below sea level.

Ricardo descended to a depth of 24 feet below sea level. His friend Martin descended 3 times as far.

If Ricardo descended to a depth of 24 feet below sea level, and Martin descended three times as far, we can calculate Martin's descent by multiplying Ricardo's depth by 3.

Martin's depth = Ricardo's depth * 3

Martin's depth = 24 feet * 3

Martin's depth = 72 feet

Therefore, Martin descended to a depth of 72 feet below sea level.

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Answer: 3.5 m/s

Step-by-step explanation:

[tex]v=\frac{vf+vi}{2}[/tex]

[tex]v=\frac{5+2}{2}[/tex]

5+2=7

7/2= 3.5

Answer:

Step-by-step explanation:

Given the expression [tex]log_81000 = log_210[/tex], to prove this expression is true using the properties of logarithm, we will follow the following steps.

Starting from the Left Hand Side:

Answer:

Where is the table because I dont see it up here?

Answer:

anything that is not -2+3x or x=2/3 is wrong

Step-by-step explanation:

Answer:

E = { x l x is a perfect square <36}

And we can rewrite it taking in count the list of all the perfect squares less than 36 and we have:

1= 1*1

4= 2*2

9 = 3*3

16 =4*4

25= 5*5

And we can rewrite the set on this way:

E= {1,4,9,16,25}

Step-by-step explanation:

For this problem we have the following set:

E = { x l x is a perfect square <36}

And we can rewrite it taking in count the list of all the perfect squares less than 36 and we have:

1= 1*1

4= 2*2

9 = 3*3

16 =4*4

25= 5*5

And we can rewrite the set on this way:

E= {1,4,9,16,25}

Answer: (-3, -2)

Step-by-step explanation:

Plug in -2 for y to find x

x - 5(-2) = 7

Multiply -5 and -2

x + 10 = 7

Subtract 10 from both sides

x = -3

The first ordered pair is (-3, -2)

Answer:

33%

Step-by-step explanation:

The multiples of 3 are 3,6,9,12

Sum is 6+14+12+1 = 33

The total is 3+6+8+11+14+16+15+12+9+5+1=100

The experimental probability is  number of multiples of 3 over the total

33/100 = 33%

Answer:

[tex]\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]

The expected values for all the categories is :

[tex] E_i =\frac{150}{3}=50[/tex]

And then the statistic would be given by:

[tex]\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4[/tex]

And the best option would be:

b. 4

Step-by-step explanation:

For this problem we have the following observed values:

Yes 40 No 60 No Opinion 50

And we want to test the following hypothesis:

Null hypothesis: All the opinions are uniformly distributed

Alternative hypothesis: Not All the opinions are uniformly distributed

And for this case the statistic would be given by:

[tex]\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]

The expected values for all the categories is :

[tex] E_i =\frac{150}{3}=50[/tex]

And then the statistic would be given by:

[tex]\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4[/tex]

And the best option would be:

b. 4

Answer: 420 words

Step-by-step explanation:

First find how much he did the first day by doing 1/5*2400=480.

Then find out how much he did the second day by doing 2400-480=1920, then doing 1920*(2/3)=1280.

Then, because he did 220 words the third day, simply do 2400-480-1280-220=420.

Hope it helps <3

Ans420 words per min

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

The double cone is a cone on top of another cone. The bottom cone has the circular base on the bottom and the tip on top. The upper cone is upside down, and the two tips touch. Since the vertical plane goes through the tips of both cones, the cross section must have a shape that  gets to a point at the middle of the height.

Answer: B. One triangle with the tip on top and an inverted triangle above it with the tips touching.

Answer:

B.

Step-by-step explanation:

answer: B. one triangle tip on top and invert above it with the top touching

Answer:

Pentagon

Step-by-step explanation:

the head is the closest I see

Answer:

for us to be able to ascertain whether a function has no limit we approach from two points which are from zero and infinity.

Step-by-step explanation:

the two best path to approach a function is to approach from zero and approach from infinity, literary what we are trying to do is approach from the smallest to the greatest and it each point we can conclude with certainty whether the function has a limit or not.

Answer:

t = d/s

t = 6.4 / 2 miles

t = 3.2 miles

Step-by-step explanation:

follow me plzzz

Answer:

10% interest.

Step-by-step explanation:

Interest I = PRT/100

If the rate R = x% we have

550 = P*x *1 / 100

and

770 = P*(x + 4) * 1 / 100

so From  first equation

Px = 55000  and from the second

Px + 4P =  77000

So Px = 77000 - 4P

Therefore  77000 - 4P = 55000

4P = 22000

P = 5,500

So x = 55000/5500 = 10%.

And  the rate for the other fund is 10 + 4 = 14%.

Answer:

Amount of money David received = £ 175

Step-by-step explanation:

Both of them share their profit in a ratio of 5:7 . Tina got £70 more than David. Let

the amount David received = a

amount Tina received = 70 + a

the total profit = 70 + 2a

Amount David received = 5/12 × 70 + 2a = a

Therefore,

5/12 × 70 + 2a = a

350 + 10a/12 = a

cross multiply

350 + 10a = 12a

collect like terms

350 = 12a - 10a

350 = 2a

divide both sides by 2

a  = 350/2

a = 175

Amount of money David received = £ 175

Answer:

Numbers 1,0,8,2 would lie on y-axis.

Step-by-step explanation:

This is because for example, (0,1)

we must prefer 0 as x-axis and 1 as y-axis. That's means left number or side will always be x-axis and right side will always be y-axis.

Answer: (0, 1)

Step-by-step explanation:

When the x is 0 is lies on the y axis.

Answer:

12.5%

Step-by-step explanation:

There is only 1 seven card from the 8 total cards.

1 out of 8.

1/8 = 0.125

P(7) = 12.5%

Answer:

12.5%

Step-by-step explanation:

Total Cards = 8

Number 7 = 1

P(7) = 1/8

In %age:

=> 12.5%

The mass of the lamina is 6 units.

The center of mass of the lamina is (X,Y) = (-3/2, 9/2).

Here,

To find the mass and center of mass of the lamina, we need to integrate the density function ρ(x, y) over the triangular region D.

The mass (M) of the lamina is given by the double integral of the density function over the region D:

M = ∬_D ρ(x, y) dA

where dA represents the differential area element.

The center of mass (X,Y) of the lamina can be calculated using the following formulas:

X = (1/M) ∬_D xρ(x, y) dA

Y = (1/M) ∬_D yρ(x, y) dA

Now, let's proceed with the calculations:

The triangular region D has vertices (0, 0), (2, 1), and (0, 3). We can define the limits of integration for x and y as follows:

0 ≤ x ≤ 2

0 ≤ y ≤ 3 - (3/2)x

Now, let's calculate the mass (M):

M = ∬_D ρ(x, y) dA

M = ∬_D 2(x + y) dA

We need to set up the double integral over the region D:

M = ∫[0 to 2] ∫[0 to 3 - (3/2)x] 2(x + y) dy dx

Now, integrate with respect to y first:

M = ∫[0 to 2] [x(y²/2 + y)] | [0 to 3 - (3/2)x] dx

M = ∫[0 to 2] [x((3 - (3/2)x)²/2 + (3 - (3/2)x))] dx

M = ∫[0 to 2] [(3x - (3/2)x²)²/2 + (3x - (3/2)x²)] dx

Now, integrate with respect to x:

[tex]M = [(x^3 - (1/2)x^4)^2/6 + (3/2)x^2 - (1/4)x^3)] | [0 to 2]\\M = [(2^3 - (1/2)(2^4))^2/6 + (3/2)(2^2) - (1/4)(2^3)] - [(0^3 - (1/2)(0^4))^2/6 + (3/2)(0^2) - (1/4)(0^3)]\\M = [(8 - 8)^2/6 + 6 - 0] - [0]\\M = 6[/tex]

So, the mass of the lamina is 6 units.

Next, let's calculate the center of mass (X,Y):

X = (1/M) ∬_D xρ(x, y) dA

X = (1/6) ∬_D x * 2(x + y) dA

We need to set up the double integral over the region D:

X = (1/6) ∫[0 to 2] ∫[0 to 3 - (3/2)x] x * 2(x + y) dy dx

Now, integrate with respect to y first:

X = (1/6) ∫[0 to 2] [x(y² + 2xy)] | [0 to 3 - (3/2)x] dx

X = (1/6) ∫[0 to 2] [x((3 - (3/2)x)² + 2x(3 - (3/2)x))] dx

X = (1/6) ∫[0 to 2] [x(9 - 9x + (9/4)x² + 6x - (3/2)x²)] dx

X = (1/6) ∫[0 to 2] [(9/4)x³ - (3/2)x⁴ + 15x - (3/2)x³] dx

Now, integrate with respect to x:

[tex]X = [(9/16)x^4 - (3/8)x^5 + (15/2)x^2 - (3/8)x^4] | [0 to 2]\\X = [(9/16)(2)^4 - (3/8)(2)^5 + (15/2)(2)^2 - (3/8)(2)^4] - [(9/16)(0)^4 - (3/8)(0)^5 + (15/2)(0)^2 - (3/8)(0)^4]\\X = [9/2 - 12 + 15 - 0] - [0]\\X = 15/2 - 12\\X = -3/2[/tex]

Next, let's calculate Y:

Y = (1/M) ∬_D yρ(x, y) dA

Y = (1/6) ∬_D y * 2(x + y) dA

We need to set up the double integral over the region D:

Y = (1/6) ∫[0 to 2] ∫[0 to 3 - (3/2)x] y * 2(x + y) dy dx

Now, integrate with respect to y first:

Y = (1/6) ∫[0 to 2] [(xy² + 2y²)] | [0 to 3 - (3/2)x] dx

Y = (1/6) ∫[0 to 2] [x((3 - (3/2)x)²) + 2((3 - (3/2)x)²)] dx

Y= (1/6) ∫[0 to 2] [x(9 - 9x + (9/4)x²) + 2(9 - 9x + (9/4)x²)] dx

Y = (1/6) ∫[0 to 2] [(9x - 9x² + (9/4)x³) + (18 - 18x + (9/2)x²)] dx

Now, integrate with respect to x:

[tex]Y= [(9/2)x^2 - 3x^3 + (9/16)x^4) + (18x - 9x^2 + (9/6)x^3)] | [0 to 2]\\Y = [(9/2)(2)^2 - 3(2)^3 + (9/16)(2)^4) + (18(2) - 9(2)^2 + (9/6)(2)^3)] - [(9/2)(0)^2 - 3(0)^3 + (9/16)(0)^4) + (18(0) - 9(0)^2 + (9/6)(0)^3)]\\Y = [18 - 24 + 9/2 + 36 - 36 + 12] - [0]\\Y= 9/2[/tex]

So, the center of mass of the lamina is (X,Y) = (-3/2, 9/2).

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Answer:

A.) NM= x

C.) LM = x√2

E.) tan (45°) = 1

Step-by-step explanation:

If the legs are both x, then the hypotenuse is equal to [tex]x\sqrt{2[/tex]

Therefore, LM= [tex]x\sqrt{2[/tex] is correct and MN= x

Disclaimer: The sum is done according to the picture attached as the question given is wrong.

The true statements regarding the given isosceles right triangle ΔLMN are:

An isosceles triangle is a triangle where two sides and their corresponding angles are equal.

A right triangle is a triangle with one angle = 90°.

An isosceles right triangle is a right-angled triangle with two legs including the right angle are equal. Their corresponding angles are equal and each of them = 45°. So, the three angles of an isosceles right triangle are 45°, 45°, and 90°, always.

In the figure, we can see that we have a ΔLMN, with ∠L = 45°, ∠M = 45°, and ∠N = 90°. Also, we can see that LN = x.

The given angles of ΔLMN determine that it is an isosceles right triangle with a right angle at N.

Since, the two legs involving the right angle, that is N, are equal, we can say that, NM = LN = x.

The hypotenuse of the ΔLMN, that is the side opposite to ∠N, that is LM, can be found using the Pythagoras theorem, by which in a right-angled triangle,

Hypotenuse² = Base² + Perpendicular².

∴ LM² = LN² + NM² = x² + x² = 2x².

or, LM = √(2x²) = x√2.

The tangent of an angle ∅, that is, tan ∅ is computed using the formula,

tan ∅ = Perpendicular/Base.

To calculate tan 45°, that is, tangent to ∠L, we take Perpendicular = NM and Base = LN.

∴ tan 45° = NM/LN = x/x = 1.

Now, we check all the given options:

∴ The true statements regarding the given isosceles right triangle ΔLMN are:

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Answer:

Step-by-step explanation:

First we must first find the LCM

The LCM of x² + 3x + 2 and (x + 2)(x + 1 ) is

x² + 3x + 2

So we have

[tex] \frac{x}{ {x}^{2} + 3x + 2 } - \frac{1}{(x + 2)(x + 1)} \\ \\ = \frac{x - 1}{ {x}^{2} + 3x + 2 } [/tex]

Hope this helps you

Answer:

The answer is OPTION D!

Step-by-step explanation:

HoPe ThIs HeLpS!

Step-by-step explanation:

let the larger number be x and smaller number be y

according to this question

x=y+33----------(1)

y+33+5y=129----------(2)

6y+33=129

y=16

x=16+33(takimg equation (1)

x=49

Answer:

Larger number: 49.

Smaller number: 16.

Step-by-step explanation:

Let's say that the larger number is represented by y, and the smaller is represented by x.

y = 33 + x

y + 5 * x = 129

(33 + x) + 5x = 129

6x + 33 = 129

6x = 96

x = 16

y = 33 + 16

y = 49

Check our work...

49 + 5 * 16 = 49 + 80 = 129

49 = 33 + 16 = 49

Since it all works out, the larger number is 49 and the smaller number is 16.

Hope this helps!

Answer:

B

Step-by-step explanation: