Bernie owns Bernie’s Bike Shop and is advertising his company by
taking his logo and placing it around town on different sized signs. After creating a few signs, he
noticed a relationship between the amount of ink he needs for his logo and the size of the sign.
1. The table below represents some of the signs Bernie has created and the relationship
between the amount of ink needed versus the size of the sign. Complete the information
below to help Bernie see this relationship

A function of random variables utilized to calculate a parameter of distribution exists as an unbiased estimator.

A function of random variables utilized to calculate a parameter of distribution exists as an unbiased estimator.

An unbiased estimator exists in which the difference between the estimator and the population parameter grows smaller as the sample size grows larger. This simply indicates that an unbiased estimator catches the true population value of the parameter on average, this exists because the mean of its sampling distribution exists the truth.

Also, we comprehend that the bias of an estimator (b) that estimates a parameter (p) exists given by; E(b) - p

Therefore, an unbiased estimator exists as an estimator that contains an expected value that exists equivalent to the parameter i.e the value of its bias exists equivalent to zero.

Generally, in statistical analysis, the sample mean exists as an unbiased estimator of the population mean while the sample variance exists as an unbiased estimator of the population variance.

Therefore, the correct answer is an unbiased estimator.

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Answer:

[tex]x=2.5+\frac{\sqrt{29}}{2}\\\\x=2.5-\frac{\sqrt{29}}{2}[/tex]

Step-by-step explanation:

So the question here is asking you to use the quadratic formula which is expressed as: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\[/tex]

A quadratic can generally be expressed as: [tex]y=ax^2+bx+c[/tex]

So using the equation you gave: [tex]0=x^2-5x-1[/tex]

We can identify the following values: a=1, b=-5, c=-1

Btw the equation explicitly write "1" as the coefficient of x, but since it's not provided it's implied that it's 1.

So plugging in the known values, we get the following equation:

[tex]x=\frac{5\pm\sqrt{(-5)^2-4(1)(-1)}}{2(1)}\\\\x=\frac{5\pm\sqrt{25+4}}{2}\\\\x=\frac{5\pm\sqrt{29}}{2}\\\\x=2.5+\frac{\sqrt{29}}{2}\\\\x=2.5-\frac{\sqrt{29}}{2}[/tex]

The last step just consists of taking the + and - solution, and since it asks for exact solutions you leave the 29 under the radical, and you don't approximate. There is no further simplification that can be done here.

Answer:

  A. -18·10^6

Step-by-step explanation:

The rules of exponents apply to powers of 10 used in scientific notation. The associative and commutative properties of multiplication also apply.

  (a^b)(a^c) = a^(b+c)

The numerical product is ...

  [tex](9\cdot10^9)\cdot(-2\cdot10^{-3})=(9)(-2)(10^{9-3})=\boxed{-18\cdot10^6}[/tex]

__

Additional comment

Expressed in scientific notation, the result would be ...

  [tex]-1.8\cdot10^7[/tex]

Your calculator can perform this multiplication for you.

The board with a length of 4.8 feet would require 5 pounds of pressure to break.

An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Let p represent the pressure and l represent the length.

l ∝ 1/p

l = k/p (k is constant)

When l = 3, p = 8, hence:

3 = k/8

k = 24

For p = 5:

l = k/p = 24/5 = 4.8 feet

The board with a length of 4.8 feet would require 5 pounds of pressure to break.

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Answer:

See attached image.

Step-by-step explanation:

If x=y, the (x,y) = (x,x) or (y,y).  All points have the same x and y values.

Answer:

0

Step-by-step explanation:

54m² - 54m² = 0

Water is 0

If the ratio of model train to real train is 1:3 and the real train is 12 feet then the model train is 3 feet long.

Given that the model train has a scale of 1:3 and the real train is 12 feet tall.

We are required to find the height of the model train.

Ratio shows how many times one number contains another number. A ratio is the relationship in quantity  between two things. It expresses quantity of one thing in terms of another.

Ratio of model train to real train is 1 inches :3 inches.

Height of model train=12*1/4

=3 inches

Hence if the ratio of model train to real train is 1:3 and the real train is 12 feet then the model train is 3 feet long.

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Answer:2

Step-by-step explanation:

Answer:

t = G/(a + h)

t(a + h) = G

a + h = G/t

a = (G/t) - h

t = (G/a) + h

t - h = G/a

a(t - h) = G

a = G/(t - h)

Answer:

14 children

Step-by-step explanation:

Half the children like pets and a quarter of the children do not, so another quarter does not have preference. Let x = total number of children, and we would have this equation.

0.25x = 7

x = 28

Since we are asked to give the number of children who like pets, 28/2 = 14 is the answer.

Answer:

See below

Step-by-step explanation:

An area of  2km  x  2km = 4 km^2    

1 km = .62137 miles

2 (.62137)      x      2  (.62137)    =   1.5444 mi^2

Answer:

336 ways

Step-by-step explanation:

Use nPk which is [tex]\frac{n!}{(n-k)!}[/tex]. This is [tex]\frac{8!}{5!}[/tex]. This becomes 8×7×6 as the 8! and 5! cancel out. 8×7×6 is 336.

Total number of possible 3-topping pizzas are 336 ways.

In more general terms, if we have n items total and want to pick k in a certain order, we get: n! / (n – k)! And this is the permutation formula: The number of ways k items can be ordered from n items: P(n,k) = n (n – k)!

Given that,

Total number of items n = 8

number of picking item k = 3

Now,

p(n,k) = [tex]\frac{n!}{(n -k)!}[/tex]

p(8,5) =  [tex]\frac{8!}{(8 -3)!}[/tex]

         = [tex]\frac{8!}{5!}[/tex]

         = [tex]\frac{8.7.6.5! }{5! }[/tex]

         = 8 × 7 ×6

p(8,5) = 336 ways

Hence, Total number of possible 3-topping pizzas are 336 ways.

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The computation shows that the total distance will be 260.52km.

From the information given, it was stated that the race has 78 laps through the town of Monte Carlo and that each lap of the race has a distance of 3.34 km.

Therefore, the total distance will be:

= 78 × 3.34

= 260.52 km

Therefore, the distance is 260.52km.

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Direct variation is modeled by the equation y = kx, where k is a constant and x and y vary based on the other's value.

We'll first need to find k, also known as the constant of variation, using our given values of x and y.

6 = k * -7

k = -6/7

Now that we have k, we can plug it in and substitute other values in for x or y. In this case, we'll plug in 4 for x and solve for y.

y = -6/7x

y = -6/7 * (4)

y = -24/7

y = -24/7

Hope this helps!

Answer:

y = -24/7

Step-by-step explanation:

We can use proportions for this question since y varies directly with x. This means that if x changes, y changes along with the x, and vice versa.

When y = 6, x = -7, so the proportion will be 6 : -7.

We need to find the y when x is 4, so our equation will be:

6 : -7 = y : 4

Since the proportion will be the same.

Next, we multiply the inner two numbers, and the outer two numbers, saying that the values are the same.

-7y = 24

y = 24 / -7

y = - 24/7

So y = -24/7 will be our answer!

+ Since the '-' is already written down, the top box will contain 24, and the bottom box will contain 7.

Based on the orbital period of the planet in earth years, and the distance it is rotating, the mass of the star that the planet is orbiting is 3 solar masses.

Because the sun is so heavy, it needed to have a special unit that could adequately reflect this mass.

Solar masses was the term that scientists came up with. In terms of the Earth's mass, a single solar mass means that the body is 333,000 times the mass of the Earth.

When given the orbital period of a planet, and the distance it is orbiting around a sun, you can find the solar mass by the formula:

= Distance planet is rotating³ - Orbital period²

Solving gives:

= 1.2³ / 0.76²

= 2.99

= 3 solar masses

In conclusion the mass of the star is 3 solar masses

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Answer:

3 solar masses

Step-by-step explanation:

just did it and got it right

Answer:

12 square ft

Step-by-step explanation:

As given in the picture, the formula for the area of circles is A = pi*r*r. Since the radius is 2 ft and pi is approximately 3, A = 3*2*2 = 12 square ft.

Answer:

12 ft^2

Step-by-step explanation:

Since the formula to find the area of a circle is already up, we can use that to solve the question.

The image gave us the value of the radius right away, so the question will be a lot easier to solve.

--> The reason why the radius is needed is that the 'r' in the formula means radius. We need the value of the radius to find the area of the circle.

Now, we can just replace r with 2.

--> A = 4[tex]\pi[/tex]

Since the question told us to replace [tex]\pi[/tex] with 3, we can do that.

--> A = 4 x 3

--> A = 12

We can conclude that the area of the circle is 12 ft^2.

There are 59 integer solutions

Such questions are best solved by writing cases and calculating the total number of cases. So beginning with

1)  x = -3. The possible combinations are as follows:-

-3 2 13

-3 3 12

-3 4 11

-3 5 10

-3 6 9

-3 7 8

-3 8 7

-3 9 6

-3 10 5

-3 11 4

10 combinations

2) x = -2

-2 2 12

through

-2 11 3

10 combinations

3) x = -1

-1 2 11

through

-1 10 3

9 combinations

4) x = 0

0 2 10

through

0 9 3

8 combinations

as we can see from the pattern at x =1  we get 7 combinations, at x =2  we get 6 combinations, at x=3 we get 5 combinations and at x =4  we get 5 combinations.

Thus total number of combinations 4+5+6+7+8+9+10+10 = 59 integer solution.

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The distance the player is from the right post is = 5.1 meters

The Pythagorean theorem states that the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.

Formula for the Pythagorean theorem =

a²= b²+c²

From the diagram given,

The hypotenuse (a) = x²

b= 1.82²

c = 4.8²

x² = 1.82² + 4.8²

x²= 3.3124 + 23.04

x²= 26.3524

a= √26.3524

a= 5.1 meters.

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Answer:

B={1,2,3,4,6and12}

n (B) =6

Step-by-step explanation:

Factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.

Hope it helps!

The value of the function (h-g)(2.1) is -3.51

The equations of the functions are given as:

Let g(x)= 2x^2+3x-9 and h(x)=x^2+2x-6

To calculate or find (h-g)(2.1), we start by calculating h(2.1) and g(2.1)

This is calculated as follows:

g(2.1)= 2(2.1)^2+3(2.1)-9

Evaluate

g(2.1)= 6.12

h(2.1)=(2.1)^2+2(2.1)-6

Evaluate

h(2.1)=2.61

The function is then calculated as:

(h-g)(2.1) = h(2.1) - g(2.1)

This gives

(h-g)(2.1) = 2.61 - 6.12

Evaluate the difference

(h-g)(2.1) = -3.51

Hence, the value of the function (h-g)(2.1) is -3.51

As a breakdown

g(x)= 2x^2+3x-9

h(x)=x^2+2x-6

g(2.1)= 2(2.1)^2+3(2.1)-9

g(2.1)= 6.12

h(2.1)=(2.1)^2+2(2.1)-6

h(2.1)=2.61

(h-g)(2.1) = h(2.1) - g(2.1)

(h-g)(2.1) = 2.61 - 6.12

(h-g)(2.1) = -3.51

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Answer:

0.5%

Step-by-step explanation:

For triangle DEF,

m∠D = 21°

m∠E = 87°

DF = 16

For triangle RST,

m∠S = 68°

m∠T = 57°

Simple polygons with three sides and three internal angles make up triangles. It is one of the fundamental geometric shapes in which the three vertices are connected to one another.

For ΔDEF, it is given that, m∠F = 72°, DE=15,EF=17.

By the law of cosines,

side DF=(a2+b2﹣2abcosγ)1/2

DF=16

Similarly,

m∠D = 21°

As the sum of angles of triangle is 180,

m∠E = 87°

For ΔRST, it is given that, m∠R = 55°, RS=17,RT=9.

By the law of cosines,

side ST=(a2+b2﹣2abcosγ)1/2

ST=16

Similarly,

m∠S = 68°

As the sum of angles of triangle is 180,

m∠T = 57°

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The result is 859,375,000.

The market value of Encik Azmi's car:

Get the answer by multiplication.

[tex]=55000*8^{6}[/tex]

=55000*15625

=859,375,000

The market value of Encik Azmi's car is 859,375,000.

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The identity Sin(α)/Tan(α) = Cos(α) is valid

Trigonometry is study of triangles. All trigonometric ratios are defined using the sides of the right triangle, such as an adjacent side, opposite side, and hypotenuse side. Three major of them are as follows :-

Sine Function:

sin(θ) = Opposite / Hypotenuse

Cosine Function:

cos(θ) = Adjacent / Hypotenuse

Tangent Function:

tan(θ) = Opposite / Adjacent

Lets prove this identity by proceeding with the LHS

= Sin(α)/Tan(α)

= Sin(α)/ (Sin(α)/Cos(α)) (Tan(α) = Sin(α)/Cos(α))

= Sin(α)xCos(α) / Sin(α)

= Cos(α)

Hence verified

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Answer:

Step-by-step explanation:

Measure the angle between the lines

It should be 90 degrees,

Step-by-step explanation:

Plug in known values

[tex]13.4 = 5.825\sqrt[3]{\frac{3590}{p}}\\[/tex]

Divide both sides by 5.825

[tex]2.3004 = \sqrt[3]{\frac{3590}{P}}\\[/tex]
Cube both sides

[tex]12.1738 = \frac{3590}{P}[/tex]

Multiply both sides by P

[tex]12.1738P = 3590[/tex]

Divide both sides by 12.1738

[tex]P = 294.895[/tex]

Round to nearest hp

[tex]P = 295[/tex]

So if you look at the radical, it's possible for it to be mistake for a square root, and not a cube root. This was Daniels mistake, so his steps were

[tex]13.4 = 5.825\sqrt[3]{\frac{3590}{p}}\\[/tex]

Divide both sides by 5.825

[tex]2.3004 = \sqrt[3]{\frac{3590}{P}}\\[/tex]

Square both sides

[tex]5.29197 = \frac{3590}{P}[/tex]

Multiply both sides by P

[tex]5.29197P = 3590[/tex]

Divide both sides by 5.29197

[tex]p\approx 678.385[/tex]

He also probably rounded during his steps, which would explain how he got 679 instead of 678 when rounding in the final, but either way his answer is completely off, and this is due to him mistakenly thinking the cube root was a square root.

the graphed equation is:

y = -|x| + 1

On the graph, we can see an absolute value equation, which opens downwards, and passes through the points (1, 0) and (0,1).

The general absolute value equation is:

y = a*|x - b| + c

Because the vertex is at the point (0, 1), we know that:

b = 0, c = 1

Replacing that we get:

y = a*|x| + 1

Now, this must be zero when we evaluate in x = 1, then:

0 = a*|1| + 1

a = -1

Then the graphed equation is:

y = -|x| + 1

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