A number cube with the numbers 1 through 6 is rolled 159 times and shows the number four 27 times. Calculate the experimental probability of rolling a four.A number cube with the numbers 1 through 6 is rolled 159 times and shows the number four 27 times. Calculate the experimental probability of rolling a four.

A half life means that half the sample decays.

If the sample size is 1 , then after one half life there would be x  * 1/2 =  1/2 of the sample left.

For the 2nd half life, multiply 1/2 by 1/2 to get 1/4.

So after 2 half lives, there is 1/4 of the sample left, which means 3/4 of the sample decayed.

The answer is 3/4

8 hours is 480 minutes

480 minutes is 2800 bottles

2800 bottles per day

28000 devided by 2800 is 100

100 days

Answer:

100 days

Step-by-step explanation:

[tex]a = \frac{b \times h}{2} [/tex]

33.6 × 2 = b×h

67.2 = b×h

h=4

67.2÷4 =b

16.8=b

answer: b=16.8inches

It takes 90 days for a single drop of water to travel the Mississippi River's entire length.

Answer:

y = 3.4

Step-by-step explanation:

Given 2 secants and a tangent drawn to the circle from an external point then

The square of the measure of the tangent is equal to the product of the external part of the secant to the entire secant.

Using the secant with measure y + 11, then

y(y + 11) = 7²

y² + 11y = 49 ( subtract 49 from both sides )

y² + 11y - 49 = 0 ← in standard form

with a = 1, b = 11 and c = - 49

Using the quadratic formula to solve for y

y = ( - 11 ± [tex]\sqrt{11^2-4(1)(-49)}[/tex] ) / 2

  = ( - 11 ± [tex]\sqrt{121+196}[/tex] ) / 2

  = ( - 11 ± [tex]\sqrt{317}[/tex] ) / 2

y = [tex]\frac{-11-\sqrt{317} }{2}[/tex] or y = [tex]\frac{-11+\sqrt{317} }{2}[/tex]

y = - 14.4 or y = 3.4

However y > 0 ⇒ y = 3.4 ( nearest tenth )

Answer:

  the associative property

Step-by-step explanation:

The associative property of addition lets you move the parentheses without changing the order of the operands.

Solve the inequality for x:

5x - 3 ≤ 7x +7

Subtract 7x from each side:

-2x -3 ≤ 7

Add 3 to each side:

-2x ≤ 10

Divide both sides by -2, also when dividing  both sides of an inequality you flip the direction of the inequality sign:

x ≥ -5

The dot will be on -5, because the inequality includes equal to, the dot is solid and is greater than, the arrow will point to the right.

The correct answer is D.

No. Asher figured that just subtracting 4 from 4x, which is 64, would get him the value of x. However, since 64=4x, one needs to divide 64 by the number of x's to get x's value. 64/4= 16, which is the value of x.

The method of solving the equation by asher is; Incorrect because she is supposed to divide directly and not subtract.

We are told that she wants to solve the equation;

4x = 64

Now, she decided to subtract 4 from both sides to get the value of x. That will not be correct because she is meant to divide both sides by the coefficient of x to get the value of x.

4x = 64

x = 64/4

x = 16

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Answer:

9841

Step-by-step explanation:

Each time the number of shaded triangles is multiplied by 3.  So this is a geometric series:

an = 1 (3)ⁿ⁻¹

The sum of the first n terms of a geometric series is:

S = a₁ (1 - rⁿ) / (1 - r)

Here, a₁ = 1, r = 3, and n = 9.

S = 1 (1 - 3⁹) / (1 - 3)

S = 9841

Answer:

on e2020 its 1 option

Step-by-step explanation:

Answer:

c(m)<=45+0.4m

Step-by-step explanation:

A linear inequality involves a linear function. It contains one of the symbols of inequality. It exactly looks like a linear equation,with the inequality sign replacing the equality sign.

According to the statement Nancy has negotiated a special rate and the maximum charge is $45.00 per day with the addition of $ 0.40 per mile.

So,

a linear inequality that models the total cost of the daily rental as a function of the total miles driven,m is:

c(m)<=45+0.4m

Answer:

8% difference I think.

Step-by-step explanation:

72 - 64 = 8.

The temperature increase from 64 degrees to 72 degrees represents a 12.5% increase. You calculate this by dividing the difference in temperature by the original temperature and then multiplying by 100.

To calculate the percent increase in temperature from 64 degrees to 72 degrees, you subtract the original temperature from the new temperature and divide by the original temperature. Then, multiply the result by 100 to get the percentage.

Here is the calculation:

Percent Increase = ((New Temperature - Original Temperature) / Original Temperature) × 100

Percent Increase = ((72 - 64) / 64) × 100

Percent Increase = (8 / 64) × 100

Percent Increase = 0.125 × 100

Percent Increase = 12.5%

Therefore, the temperature has increased by 12.5%.

The remainder theorem says [tex]x-c[/tex] is a factor of a polynomial [tex]p(x)[/tex] if [tex]p(c)=0[/tex]. So all you need to do is check the value of [tex]x^3+7x^2+4x-12[/tex] when [tex]x=-6[/tex]. We have

[tex](-6)^3+7(-6)^2+4(-6)-12=0[/tex]

so [tex]x+6[/tex] is indeed a factor.

Answer:

  32. -30°

  33. 45° or 135°

  34. 90°

Step-by-step explanation:

The table below shows a short list of trig function values.

32. -tan(x) = tan(-x)

33. -cos(x) = cos(180°-x)

34. sec(x) = 1/cos(x). 1/0 is "undefined".

The values shown above are the ones that are in the range of the inverse trig functions: arctan (-90°, 90°), arccos [0°, 180°], arcsec [0°, 90°)∪(90°, 180°].

[tex]32.\quad tan\theta=-\dfrac{\sqrt3}{3}\\\\.\qquad \dfrac{sin\theta}{cos\theta}=-\dfrac{\sqrt3}{3}\\\\\text{Since there is no "3" on the Unit Circle, un-rationalize the denominator:}\\.\qquad \dfrac{sin\theta}{cos\theta}=-\dfrac{\sqrt3}{3}\bigg(\dfrac{\sqrt3}{\sqrt3}\bigg)\implies \dfrac{sin\theta}{cos\theta}=-\dfrac{3}{3\sqrt3}=-\dfrac{1}{\sqrt3}\\\\\implies sin\theta =\pm\dfrac{1}{2}\quad and \quad cos\theta = \pm\dfrac{\sqrt3}{2}\quad and \text{ coordinate is in Quadrant 2 or 4}[/tex]

[tex]\text{Look on the Unit Circle (below) for coordinates }\bigg(\dfrac{-\sqrt3}{2},\dfrac{1}{2}\bigg)\ and\ \bigg(\dfrac{\sqrt3}{2},\dfrac{-1}{2}\bigg)\\\\\bold{Answer:}\large\boxed{150^o\ and\ 330^o\implies \dfrac{5\pi}{6}\ and\ \dfrac{11\pi}{6}}[/tex]

[tex]33.\quad cos^2\theta=\dfrac{1}{2}\\\\\\.\qquad \sqrt{cos^2\theta}=\sqrt{\dfrac{1}{2}}\\\\\\.\qquad cos\theta=\pm\dfrac{1}{\sqrt2}\\\\\\\text{Rationalize the denominator:}\\.\qquad cos\theta=\pm\dfrac{1}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)\implies cos\theta=\pm\dfrac{\sqrt2}{2}\\\\\\\text{Look on the Unit Circle to find when }cos\theta=\dfrac{\sqrt2}{2}\ and\ \dfrac{-\sqrt2}{2}[/tex]

[tex]\bold{Answer:}\large\boxed{45^o, 135^o, 225^o, 315^o\implies \dfrac{\pi}{4}, \dfrac{3\pi}{4}, \dfrac{5\pi}{4}, \dfrac{7\pi}{4}}[/tex]

[tex]34.\quad sec\theta=\text{unde fined}\implies sec\theta=\dfrac{1}{0}\\\\\\.\qquad \dfrac{1}{cos\theta}=\dfrac{1}{0}\implies cos\theta=0\\\\\\\text{Look on the Unit Circle to find when }cos\theta=0\\\\\bold{Answer:}\large\boxed{90^o\ and\ 270^o\implies\dfrac{\pi}{2}\ and\ \dfrac{3\pi}{2}}[/tex]

Answer:

an = 15 (1/5)^(n-1)

Step-by-step explanation:

In a geometric series, each term is multiplied by a common ratio to get the next term.  Such that:

an = a₁ (r)^(n-1)

Here, the first term, a₁, is 15.  The common ratio, r, is 1/5, because each term is divided by 5 to get the next term.  So:

an = 15 (1/5)^(n-1)

Your answer is correct, well done!

I think this is an example of it

Answer:

The required inequality is [tex]y<\frac{2}{3}(x)-1[/tex].

Step-by-step explanation:

From the given graph it is clear that the related line passes through the points (-3,-3) and (3,1).

If a line passes through two points, then the equation of line is

[tex]y-y_1=\frac{y-y_1}{x-x_1}(x-x_1)[/tex]

The equation of related line is

[tex]y-(-3)=\frac{1-(-3)}{3-(-3)}(x-(-3))[/tex]

[tex]y+3=\frac{4}{6}(x+3)[/tex]

[tex]y+3=\frac{2}{3}(x+3)[/tex]

[tex]y+3=\frac{2}{3}(x)+2[/tex]

Subtract 3 from both the sides.

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

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

The equation of related line is [tex]y=\frac{2}{3}(x)-1[/tex]. The related line is a dotted and the shaded region is below the line. So, the sign of inequality is <.

The required inequality is

[tex]y<\frac{2}{3}(x)-1[/tex]

Therefore the required inequality is [tex]y<\frac{2}{3}(x)-1[/tex].

Answer:

314 m³

Step-by-step explanation:

The volume (V) of a cone is calculated using the formula

V = [tex]\frac{1}{3}[/tex]πr²h

where r is the radius and h the perpendicular height

To find h use the right triangle from the vertex to the midpoint of the base and the radius.

Using Pythagoras' identity on the right triangle

where the slant height is the hypotenuse, then

h² + 5² = 13²

h² + 25 = 169 ( subtract 25 from both sides )

h² = 144 ( take the square root of both sides )

h = [tex]\sqrt{144}[/tex] = 12, hence

V = [tex]\frac{1}{3}[/tex]π × 5² × 12

   = π × 25 × 4 = 100π ≈ 314 m³

Final answer:

Ken will require 150 cm² of decorative paper to cover his triangular prism souvenir. This is calculated by determining the area of the two triangular bases and the three rectangular sides and adding them together.

Explanation:

To calculate the total area of decorative paper Ken requires to cover his triangular prism souvenir, we need to consider the area of all the sides of the prism. The prism has two triangular bases and three rectangular sides.

For the triangular bases, we use the formula for the area of a triangle: A = (base × height) / 2. Since we have two bases with base=5 cm (a) and height=6 cm (h), the total area for the two triangular bases would be

2 × (5 cm × 6 cm) / 2 = 30 cm²

For the three rectangular sides, the dimensions are height (h=6 cm) and width (w=10 cm), plus two sides with a side length equal to the height of the triangular base. The area of each rectangle is given by length × width. Therefore, the total area for the rectangular sides is:

2 × (5 cm × 6 cm) + (10 cm × 6 cm) = 60 cm² + 60 cm² = 120 cm²

Adding the areas of the bases and the sides, we obtain the total area of decorative paper needed:

Total area = Area of bases + Area of sides = 30 cm² + 120 cm² = 150 cm²

Therefore, Ken will require 150 cm² of decorative paper to cover his triangular prism souvenir.

Answer:

2 : 3

Step-by-step explanation:

Calculate the ratio of corresponding sides

AB : LM = 4 : 6 = 2 : 3

AD : LO = 2 : 3

DC : ON = 4 : 6 = 2 : 3

CB : NM = 2 : 3

The ratio of corresponding sides is 2 : 3

Answer:

No, because each group of n items does not have an equal chance of being selected.

Step-by-step explanation:

Answer:0.1

Step-by-step explanation:

The answer is:

The correct option is:

C) [tex]4^{3}*4^{4}=4^{7}[/tex]

To solve the problem, we need to remember the product of powers with the same base property, the property is defined by the following relation:

[tex]a^{m}*a^{n}=a^{m+n}[/tex]

If we are multiplying two or more powers with the same base, we must keep the base and add/subtract the exponents.

So, we are given the expression:

[tex]4^{3}*4^{4}[/tex]

We can see that both powers have the same base (4), so solving we have:

[tex]4^{3}*4^{4}=4^{4+3}=4^{7}[/tex]

Hence, we have that the correct option is:

C) [tex]4^{3}*4^{4}=4^{7}[/tex]

Have a nice day!

Answer:

The correct answer is option C

4^7

Step-by-step explanation:

Points to remember

Identities

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾

xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾

x⁻ᵃ = 1/xᵃ

To find the correct option

It is given that,

4^3 * 4^4

⇒ 4³ * 4⁴

By using identities we can write,

4³ * 4⁴  = 4⁽³ ⁺ ⁴)

 = 4⁷

Therefore the correct option is option C.  4^7

Answer:

Step-by-step explanation:

Let's calculate the probability of selecting a blue shirt from a total of 10 shirts:

It's 5/10, or 0.5, which stems from there being 5 blue shirts among the 10 Jeremy owns.  50/50 is not a standard way of expressing probability; 0.5 is proper.

Answer: Second Option

[tex]P =0.00476[/tex]

Step-by-step explanation:

The probability sought is calculated by calculating the quotient between the number of possible ways to select 4 seniors from a group of 4 seniors among the number of ways to select 4 seniors from a group of 10 people.

So:

[tex]P =\frac{4C4}{10C4}[/tex]

Where

[tex]nCr = \frac{n!}{r!(n-r)!}[/tex]

is the number of ways in which a number r of people can be selected from a group of n people

Then

[tex]P =\frac{\frac{4!}{4!(4-4)!}}{\frac{10!}{4!(10-4)!}}\\\\\\P =\frac{1}{\frac{10!}{4!(10-4)!}}\\\\P =\frac{1}{210}\\\\P=0.00476[/tex]

Following the equation

[tex]V(t) = V_0(1-r)^t[/tex]

We start with an initial price of

[tex]V(0)=V_0[/tex]

and we're looking for a number of years t such that

[tex]V(t)=\dfrac{V_0}{2}[/tex]

If we substitute V(t) with its equation, recalling that

[tex]r = 0.075 \implies 1-r = 0.925[/tex]

we have

[tex]V_0\cdot (0.925)^t=\dfrac{V_0}{2} \iff 0.925^t = \dfrac{1}{2} \iff t = \log_{0.925}\left(\dfrac{1}{2}\right)\approx 8.89[/tex]

So, you have to wait about 9 years.

Final answer:

The expression to determine the number of years it takes for the car to reach a value that is 50% of its purchase price is t = ln(0.5) / ln(1 - 0.075), using the given formula V = Vo(1 - r)^t.

Explanation:

To determine the number of years t after purchase for the car to reach a value that is 50% of its purchase price, we can use the model V = Vo(1 - r)^t where V is the car's value after t years, Vo is the original purchase price, r is the constant annual rate of decrease, and t is the number of years.

V is set to be 50% of Vo, which can be written as V = 0.5Vo, and we know the constant annual rate of decrease r is 0.075. Plugging these values into the formula gives us:

0.5Vo = Vo(1 - 0.075)^t

Dividing both sides by Vo and taking the natural logarithm of both sides, we obtain:

ln(0.5) = ln((1 - 0.075)^t)

Using the properties of logarithms, we can rewrite this as:

ln(0.5) = t * ln(1 - 0.075)

Solving for t yields:

t = ln(0.5) / ln(1 - 0.075)

This expression can be used to find the number of years it takes for the car to be worth half of its purchase price.

Answer:

B

Step-by-step explanation:

Euler's formula for polyhedra states that

F + V - E = 2

where F is faces, V is vertices and E is edges

Substitute the values given and solve for F, that is

F + 13 - 26 = 2

F - 13 = 2 ( add 13 to both sides )

F = 15 → B

The correct option is (B) 15

Euler's formula states the relationship between the number of Faces, Edges and Vertices of any polyhedron. It is given as

[tex]F+V=E+2[/tex]

where

[tex]F=\text{number of faces}\\V=\text{number of vertices}\\E=\text{number of edges}[/tex]

From the question

[tex]V=13,E=26[/tex]

so

[tex]F+V=E+2\\F+13=26+2\\F=26+2-13=15[/tex]

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Answer:

The graph  attached below is for r=2+ 2sin θ where θ=pi

Step-by-step explanation

The coordinates in a polar equation are written as (r,θ)

r= radius and θ is the angle

⇒⇒⇒ so this mean we rotate θ radians and of the size r units

In our case assume θ=[tex]\pi[/tex] where 0≤θ≤2[tex]\pi[/tex]

Answer:

B. 3.

Step-by-step explanation:

At the limit we can take the numerator  to be √(9x^4) = 3x^2

The function is of the form ∞/ ∞ as x approaches ∞ so we can apply l'hopitals rule:

Differentiating top and bottom we have   6x / 2x - 3. Differentiating again we get 6 / 2 = 3.

Our limit as x  approaches infinity  is 3.

The limit of [tex]\(\sqrt{9x^4 + 1}/(x^2 - 3x + 5)\)[/tex] as x approaches infinity is 3, after comparing the highest powers of x in both the numerator and the denominator and simplifying.

To find the limit of the given function [tex]\(\displaystyle\lim_{x \to \infty} \frac{\sqrt{9x^4+1}}{x^2 -3x + 5}\)[/tex] as x approaches infinity, we can use the property of limits involving infinity. We need to compare the highest powers of x in both the numerator and the denominator. The highest power of x in the numerator under the square root is x⁴, and outside the square root, it will be x². In the denominator, the highest power is x². If we divide the numerator and the denominator by x², we get:

[tex]\[ \frac{\sqrt{9x^4+1}}{x^2 -3x + 5} = \frac{\sqrt{\frac{9x^4}{x^4}+\frac{1}{x^4}}}{\frac{x^2}{x^2} -\frac{3x}{x^2} + \frac{5}{x^2}} = \frac{\sqrt{9+\frac{1}{x^4}}}{1 -\frac{3}{x} + \frac{5}{x^2}} \][/tex]

As x approaches infinity, the terms [tex]\(\frac{1}{x^4}\), \(\frac{3}{x}\), and \(\frac{5}{x^2}\)[/tex] approach zero, and we are left with:

[tex]\[ \frac{\sqrt{9}}{1} = 3 \][/tex]

Therefore, the limit of the given function as x approaches infinity is 3, which corresponds to option (B).

Answer:

45 feet

Step-by-step explanation:

This is a classic right triangle trig problem.  We have a reference angle, which is the angle made between the ground and the belt, of 32 degrees.  The height up the side of the barn, which is the side across from the reference angle, is 24 feet.  Which of our trig ratios relates side opposite to the hypotenuse?  It's the sin ratio, so let's set it up and solve for the length of the belt, which is the hypotenuse of the right triangle.

[tex]sin(32)=\frac{24}{x}[/tex]

Doing some algebraic acrobatics that with we get

[tex]x=\frac{24}{sin(32)}[/tex]

Plug that into your calculator in degree mode and you'll get 45.28991.  Rounded to the nearest foot is 45 feet.

The length of the conveyor is approximately 45 feet.

The subject of the question is Mathematics, and it deals with determining the length of a conveyor belt that makes an angle with the horizontal. This type of problem involves trigonometry, specifically the use of sine, cosine, or tangent functions to find the length of the hypotenuse of a right-angled triangle.

To find the length of the conveyor belt, we consider the belt as the hypotenuse of a right-angled triangle, with the vertical height of the barn door as the opposite side, and the angle given as the angle between the belt (hypotenuse) and the ground (adjacent side).

The height of the barn door is 24 feet, and the angle between the belt and the ground is 32 degrees. We can use the sine function (sin) since we have the opposite side and need to find the hypotenuse (length of the conveyor belt).

The formula to find the length (L) of the conveyor belt is:

L = height / sin(angle)

L = 24 feet / sin(32 degrees)

L = 24/0.5299

L = 45.29 feet

Answer:

see explanation

Step-by-step explanation:

Using the coefficients of the polynomial and evaluating for h = - 3

- 3 | 1   - 4   - 9   36

      ↓   - 3   21   - 36

      -------------------------

       1   - 7   12   0 ← remainder

Since remainder is 0 then (x + 3) is a factor, so

y = (x + 3)(x² - 7x + 12)

To factor the quadratic

Consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term (- 7)

The factors are - 4 and - 3, since

- 4 × - 3 = + 12 and - 4 - 3 = - 7, then

x² - 7x + 12 = (x - 4)(x - 3), and

y = (x + 3)(x - 4)(x - 3)

Answer:

B) 1452π units³

Step-by-step explanation:

To find the Volume of a cylinder, use this formula:

V (cylinder) = πr²h

Note that:

r = radius of the circle (base) = 11

h = height of the cylinder = 12

π = 3.14

Plug in the corresponding numbers to the corresponding variables.

V = (3.14)(11)²(12)

Remember to follow PEMDAS. First, solve for the power, then solve left -> right.

V = (3.14)(121)(12)

V = (379.94)(12)

V = 4559.28 units³

Note that the answer choices have π  in them, divide π from the answer, and add to the answer.

V = (4559.28)/3.14 = 1452π units³

B) 1452π units³ is your answer.

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