If the coefficient of determination for a data set containing 24 points is 0.5,
12 of the data points must lie on the regression line for the data set.
A. True
O B. False
SUBMIT

Answer:

Step-by-step explanation:

125 = 5 *5 * 5 = 5³

8 = 2 * 2 *2 = 2³

125x⁶ - 8 = 5³(x²)³ - 2³

               = (5x²)³ - 2³     { a³ - b³ = (a -b)(a² + ab + b²)

               = (5x² - 2) ([5x²]² + 5x²*2 + 2²)

                 = (5x² - 2)(25x⁴ + 10x² + 4)

Hint: (5x²)² = 5² * (x²)² = 25* x²ˣ² = 25x⁴

Hi there! :)

Answer:

[tex]\huge\boxed{\frac{1}{25}}[/tex]

When evaluating an expression with a negative exponent, the reciprocal will need to be taken. Therefore:

[tex]5^{-2} = \frac{1}{5^{2} } = \frac{1}{25}[/tex]

Company a samples 16 workers, and their average time with the company is 5.2 years with a standard deviation of 1.1. Company b samples 21 workers and their average time with the company is 4.6 years with a standard deviation 4.6 years

The populations are normally distributed.  Determine the:

Hypothesis in symbolic form?

Determine the value of the test statistic?

Find the critical value or value?

determine if you should reject null hypothesis or fail to reject?

write a conclusion addressing the original claim?

Answer:

Step-by-step explanation:

GIven that :

Company A

Sample size n₁ = 16 workers

Mean [tex]\mu[/tex]₁ = 5.2

Standard deviation [tex]\sigma[/tex]₁ = 1.1

Company B

Sample size n₂ = 21 workers

Mean [tex]\mu[/tex]₂ = 4.6

Standard deviation [tex]\mu[/tex]₂ = 4.6

The null hypothesis and the alternative hypothesis can be computed as follows:

[tex]H_o : \mu _1 = \mu_2[/tex]

[tex]H_1 : \mu _1 > \mu_2[/tex]

The value of the test statistics can be determined by using the formula:

[tex]t = \dfrac{\overline {x_1}- \overline {x_2}}{\sqrt{\sigma p^2( \dfrac{1}{n_1}+\dfrac{1}{n_2})}}[/tex]

where;

[tex]\sigma p^2= \dfrac{(n_1 -1) \sigma_1^2+ (n_2-1)\sigma_2^2}{n_1+n_2-2}[/tex]

[tex]\sigma p^2= \dfrac{(16 -1) (1.1)^2+ (21-1)4.6^2}{16+21-2}[/tex]

[tex]\sigma p^2= \dfrac{(15) (1.21)+ (20)21.16}{35}[/tex]

[tex]\sigma p^2= \dfrac{18.15+ 423.2}{35}[/tex]

[tex]\sigma p^2= \dfrac{441.35}{35}[/tex]

[tex]\sigma p^2= 12.61[/tex]

Recall:

[tex]t = \dfrac{\overline {x_1}- \overline {x_2}}{\sqrt{\sigma p^2( \dfrac{1}{n_1}+\dfrac{1}{n_2})}}[/tex]

[tex]t = \dfrac{5.2- 4.6}{\sqrt{12.61( \dfrac{1}{16}+\dfrac{1}{21})}}[/tex]

[tex]t = \dfrac{0.6}{\sqrt{12.61( \dfrac{37}{336})}}[/tex]

[tex]t = \dfrac{0.6}{\sqrt{12.61(0.110119)}}[/tex]

[tex]t = \dfrac{0.6}{\sqrt{1.38860059}}[/tex]

[tex]t = \dfrac{0.6}{1.178388981}[/tex]

t = 0.50917

degree of freedom df = ( n₁ + n₂ - 2 )

degree of freedom df = (16 + 21 - 2)

degree of freedom df = 35

Using Level of  significance ∝ = 0.05, From t-calculator , given that t = 0.50917 and degree of freedom df = 35

p - value =  0.3069

The critical value [tex]t_{\alpha ,d.f}[/tex] = [tex]t_{0.05 , 35}[/tex] = 1.6895

Decision Rule: Reject the null hypothesis if the test statistics is greater than the critical value.

Conclusion: We do not reject the null hypothesis because, the test statistics is lesser than the critical value, therefore we conclude that there is  no sufficient information that the claim that company a retains it workers longer than more than company b.

Answer:

I would say about 5 times but I am not sure so if it is wrong am sorry.

Answer:

b

Step-by-step explanation:

Answer:

80 degrees

Step-by-step explanation:

m∠4 is the same as m∠2

I measured it with a protracter

( plz mark me as brainliest, that would be most appreciated! )

Answer:

x<10

Step-by-step explanation:

On the number line it shows that the dot is at 10.  Since the dot is not colored in, we know it's not greater/less than or equal to.  Greater/less than or equal to is where it shows the symbol, but it's underlined, like this: ≤.  Only when the dot is colored in, is there a possibility it is greater/less than or equal to.  So it can be greater than or less than something.  Since it starts at 10 and is decreasing, it is going to be less than.

X will be less than something.  And because the dot is at 10, it means 10 was the start.  X is less than 10 since the arrow is pointing to where the numbers are decreasing.  So, x<10.

Answer:

408 bottles

Step-by-step explanation:

the machine can fill 136 bottles in 1 hour, 136×3=408

Answer:

408

Step-by-step explanation:

680 bottles in 5 hours

in three hours:

1 hour =680/5=136

in three hours:it will be 136*3=408

Answer:

Aw what animal

Step-by-step explanation:

Srry I need pointse

Answer:

B. 1/2

Step-by-step explanation:

y = ax^2 + bx + c

14 = a(0)^2 + b(0) + c

c = 14

10.5 = a(1)^2 + b(1) + 14

10.5 = a + b + 14 ____(i)

8 = a(2)^2 + b(2) + 14

8 = 4a + 2b + 14

4 = 2a + b + 7 ___ (ii)

i - ii

10.5 - 4 = -a + 7

6.5 = -a + 7

a = 7- 6.5

a = 0.5

Value of a in the quadratic function is 0.5

In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree

Given,

Quadratic function

y = [tex]ax^{2}+bx+c[/tex]

Consider values in the table x= 0 and  y =14

[tex]14=a(0)^{2}+b(0)+c\\ c=14[/tex]

Consider x=1 and y = 10.5

[tex]10.5=a(1^{2})+b(1)+c\\ a+b=10.5-14\\a+b=-3.5[/tex]

Consider x=2 and y =8

[tex]8=a(2^{2})+b(2)+c\\ a\\8=4a+2b+14\\4a+2b=-6\\2a+b=-3[/tex]

Subtract a + b= -3.5 from 2a + b= -3

a=-3--3.5=0.5

Hence, the Value of a in the quadratic function is 0.5

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Answer:

both angles are the same, so you can use it interchangeably in proving.

But i suggest you to mantain only one, because it's easier to understand and it looks better.

Answer:

d

Step-by-step explanation:answer is d on edg

Answer:

The four legged stool is the one that rocks slightly from side to side. The three legged stool does not.

Step-by-step explanation:

The four legged stool is the one that rocks slightly because the three legs determine a plane, and the three legs are stuck on that single plane.

Answer:

18y^3 + 24y^5.

Step-by-step explanation:

6y^3(3 + 4y^2)

= 6*3 y^3 + 6*4 y^(3+2)

= 18y^3 + 24y^5.

Answer:

Step-by-step explanation:

Let the price of the room be p

Let the size of the room be s

To find the size of a kitchen that costs $3,824.00 we must first find the relationship between them

The statement

The price of tiling a room varies directly as the size of the room is written as

where k is the constant of proportionality

when

p = $4,224.00

s = 264 square feet

Substitute the values into the expression to find k

That's

4224 = 264k

Divide both sides by 264

k = 16

So the formula for the variation is

when

p = 3824

[tex]s = \frac{p}{16} [/tex]

[tex]s = \frac{3824}{16} [/tex]

s = 239

The final answer is

239 square feet

Hope this helps you

Answer:

16.2788 feet

Step-by-step explanation:

a²+b²=c²

3²+16²=c²

9+256=c²

265=c²

c=√265

c=16.2788 feet

If the ladder is 3 feet from the base of the house and the top is 16 feet from the base then the length of ladder is approximately 16.2788 feet long.

Pythagoras theorem says that in a right angled triangle the square of hypotenuse of triangle is equal to the sum of squares of base and perpendicular of that respective triangle.

[tex]H^{2} =P^{2} +B^{2}[/tex] where H is hypotenuse, P is perpendicular, B is base of triangle.

If a painter leans a ladder against a wall then it forms a right angled triangle so in this we will apply pythagoras theorem to find the length of ladder.

let the length of ladder be h so,

[tex]h^{2} =3^{2} +16^{2}[/tex]

[tex]h^{2} =9+256[/tex]

[tex]h^{2} =265[/tex]

h=[tex]\sqrt{265}[/tex]

h=16.2788 feet.

Hence the length of ladder is 16.2788 feet.

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Answer:

[tex]\boxed{478.02}[/tex]

Step-by-step explanation:

→ First understand what Pythagoras theorem is

Pythagoras is a theorem used to find the hypotenuse (the side opposite to the right-angle) of a triangle. We would need the base lengths as well the height in order to use Pythagoras.

→ State the formula and identify the letters

a² + b² = c² ⇒ where 'a' is 380cm, 'b' is 290cm and 'c' is what we are trying to work out

→ Substitute in the values into the formula

380² + 290² = c²

⇒ Simplify

144400 + 84100 = c²

⇒ Collect the numbers together

228500 = c²

⇒ Square root both sides to find 'c'

478.0167361 = c

→ The length of the diagonal is 478.02

Answer:

x = - 3 ± [tex]\sqrt{10}[/tex]

Step-by-step explanation:

Given

4x² + 24x = 4 ( divide through by 4 )

x² + 6x = 1

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(3)x + 9 = 1 + 9

(x + 3)² = 10 ( take the square root of both sides )

x + 3 = ± [tex]\sqrt{10}[/tex] ( subtract 3 from both sides )

x = - 3 ± [tex]\sqrt{10}[/tex]

Answer:

X=1/8

Step-by-step explanation:

Calculate the product 4x×2 + 24x = 4

Collect like terms 8x + 24x = 4

Divide both sides of the equation by "32" 32x = 4

Solution x = 1/8

Answer:

(D) [tex]y=\frac{18}{6}x[/tex]

Step-by-step explanation:

We will be able to know if an equation has a constant of proportionality of 3 if the constant which is being multiplied by x is equal to 3.

[tex]\frac{8}{5} =1.6[/tex] so no for A.

[tex]\frac{1}{3} = 0.\overline{33}[/tex] so no for B too.

[tex]\frac{1}{4} = 0.25[/tex] so no for C as well.

[tex]\frac{18}{6} = 3[/tex], so D works.

Hope this helped!

Answer:

298.3 square centimeters

Step-by-step explanation:

We are given

Slant height (l)= 14cm

Radius (r)= 5cm

Since we are given the slant height ,

the formula for surface area of a cone =

πrl + πr²

πr(l + r)

π = 3.14

Hence,

3.14 × 5(14 + 5)

3.14 × 5(19)

= 298.3 square centimeters

Answer:

C. $128

Step-by-step explanation:

320 x 0.5 = 160

320 - 160 = 160

160 x 0.20 = 32

160 - 32 = 128

Answer:

Below

Step-by-step explanation:

sin(2x) = 2 ×cos(x)× sin(x)

● sin(x) = 2 × cos(x) × sin(x)

● 2 × cos(x) = 1

● cos (x) = 1/2

So we can deduce that:

● x = Pi/3 + 2*k*Pi

● or x = -Pi/3 + 2*k*Pi

K is an integer

The Solution of x:

x = π/3 + 2πn, where n is an integer.

x = 2π/3 + 2πn, where n is an integer.

In degrees:

x = 60° + 360°n, where n is an integer.

x = 120° + 360°n, where n is an integer.

To solve the equation sin(2x) = sin(x), we can use the properties of trigonometric functions.

First, let's simplify the equation using the double angle identity for sine:

sin(2x) = 2sin(x)cos(x).

Now we can rewrite the equation as:

2sin(x)cos(x) = sin(x).

2cos(x) = 1.

Dividing both sides of the equation by cos(x), we get:

2 = 1/cos(x).

Now, we can find the value of cos(x) by taking the reciprocal of both sides:

cos(x) = 1/2.

From the unit circle or trigonometric values,

we know that cos(x) = 1/2 corresponds to angles of π/3 or 2π/3 (in radians) or 60° or 120° .

So, the solutions for x are:

x = π/3 + 2πn, where n is an integer.

or

x = 2π/3 + 2πn, where n is an integer.

In degrees:

x = 60° + 360°n, where n is an integer.

or

x = 120° + 360°n, where n is an integer.

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Answer:

f(x) = - 3x + 4

Step-by-step explanation:

Note that y = f(x)

Rearrange making y the subject

9x + 3y = 12 ( subtract 9x from both sides )

3y = - 9x + 12 ( divide all terms by 3 )

y = - 3x + 4 , that is

f(x) = - 3x + 4

Answer:

95 minutes

Step-by-step explanation:

Add together how long it has been cooking plus how long it needs to cook

48+47 = 95

95 minutes

Answer:

155

Step-by-step explanation:

Add 60 and 48 to get 108 then add 108 and 47 to get 155

Answer:

A. 9

Step-by-step explanation:

Lori works as a cartoonist for a teen magazine. The time she spends sketching is given by the equation m=12s where m is the number of minutes and s is the number of sketches if Lori made 3/4 of a sketch she spent A.9 B.12 C.16 D.20 minutes sketching

Solution

m= number of minutes

s= number of sketches

Equation is

m=12s

If Lori made 3/4 of the sketch, then the time spent is ?

s=3/4

m=?

m=12s

m= 12 × 3/4

=36/4

=9

m=9

If Lori made 3/4 of the sketch, then she spent 9 minutes sketching.

Answer:

I hope this helps

Step-by-step explanation:

Answer:

third option

Step-by-step explanation:

Given

f(x) = [tex]\frac{5x+5}{x^2+x-2}[/tex]

The denominator cannot be zero as this would make f(x) undefined.

Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.

solve x² + x - 2 = 0 ← in standard form

(x + 2)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 1 = 0 ⇒ x = 1

The vertical asymptotes are x = 1 and x = - 2

Answer:

C. 10cm

Step-by-step explanation:

Bryce is making a model building.

He raises the walls of the building

by 2 centimeters five times. By how

many centimeters does Bryce raise

the walls all together?

(A) 2 cm

(C) 10 cm

(B) 5 cm

(D) 20 cm

Bryce raises the walls of the building 2centimeters five times

This means, he raises the walls 2centimeters five different times

By how many centimeters does Bryce raise the walls all together?

We can solve this by finding the product of 2centimeters five times

The total centimeters Bryce raises the walls altogether= 2 centimeters × 5 times

=2cm × 5

=10cm

Answer:

[tex]x=70[/tex]

Step-by-step explanation:

If we know that the LCM of 10, 14 and x will be 70, that means x has to be a factor of 70.

First, let's find the multiples of 10 and 14 until they equal 70.

[tex]10: 10,20,30,40,50,60,70[/tex]

[tex]14:14,28,42,56,70[/tex]

Since we're asking for the greatest value of x, that means that x has to be smaller or equal to than 70 but still large enough to be the greatest.

Hey, isn't 70 a factor of 70? The remainder gets to 1 which is a whole number, so 70 is a multiple of 70.

So, [tex]x = 70[/tex].

Hope this helped!

Answer:

x = 35

Step-by-step explanation:

70 factored is 2 x 5 x 7

x  = 35

Answer:

108 inches and 2160 inches

Step-by-step explanation:

108 inches = 274.32 cm

180 inches = 457.2 cm

The area of the mural, A1 = 274.32 X 457.2 = 125419.1 cm²

Let the area of the photograph = A2

The scale A1 to A2,

1/12 = A1/A2

1/12 = 125419.1/A2

∴ A2 = 12 X 125419.1 = 1505029.2 cm²

For their lenghs

1/12 = L1/L2

1/12 = 457.2/L2

L2 = 12 X 457.2 = 5486.4 cm (or 2160 inches)

The width of  the photograph

1505029.2/5486.4 = 274.3 cm ( 108 inches)

Answer:

She can go 120 km before she runs out of fuel

It will take 2 hours.

Step-by-step explanation:

150 km is the distance

60 km/ h is the speed

The gas tank is 20 liters

We can go 6 km per liter

Fuel costs .60 dollars per liter

We need to determine how far she can go on a tank of gas

20 liters * 6 km / liter = 120 km

She can go 120 km before she runs out of fuel

120 km  = 60 km/ h  *  x hours

Divide each side by 60

120/60 = x

2 hours

Answer:

Hopes this helps!

Step-by-step explanation: