Use the binomial expression (p+q)n

to calculate a binomial distribution with n = 5 and p = 0.3.

Answer: 45 in²

Step-by-step explanation:

3 stamps by 4 stamps = 12 stamps

9 in / 12 stamps = 0.75 in/stamp

6 stamps by 10 stamps = 60 stamps

60 stamps * 0.75 in/stamp = 45 in²

Answer:

The series is convergent answer ⇒ (a)

Step-by-step explanation:

* The series is -8/5 + 32/25 + -128/125 + ........

- It is a geometric series with:

- first term a = -8/5 and common ratio r = 32/25 ÷ -8/5 = -4/5

* The difference between the convergent and divergent

  in the geometric series is :

- If the geometric series is given by  sum  = a + a r + a r² + a r³ + ...

* Where a is the first term and r is the common ratio

* If |r| < 1 then the following geometric series converges to a / (1 - r).  

- Where a/1 - r is the sum to infinity

* The proof is:

∵ S = a(1 - r^n)/(1 - r) ⇒ when IrI < 1 and n very large number

∴ r^n approach to zero

∴ S = a(1 - 0)/(1 - r) = a/(1 - r)

∴ S∞ = a/1 - r

* If |r| ≥ 1 then the above geometric series diverges

∵ r = -4/5

∴ IrI = 4/5

∴ IrI < 1

∴ The series is convergent

The ratio of successive terms leads to a limit of 4/5, which is less than 1. Hence, the series is convergent.

Convergence or Divergence of a Series

To determine whether the series -8/5+32/25-128/125+... is convergent or divergent, we observe the series' structure and apply the ratio test. For a series ∑a_n, the ratio test considers the limit L = lim (n→∞) |a_(n+1) / a_n|.

Let's compute this for our series:

[tex]a_n = (-1)^{(n+1)} * 8 * (4/5)^{(n-1)}[/tex]

Compute [tex]a_(n+1): a_(n+1) = (-1)^{(n+2)} * 8 * (4/5)^n[/tex]

Calculate |a_(n+1) / a_n| = [tex]|(-1)^{(n+2)} * 8 * (4/5)^n / (-1)^{(n+1)} * 8 * (4/5)^{(n-1)}| = |(4/5)|[/tex]

The limit L = |(4/5)| = 4/5 which is less than 1.

Since L < 1, by the ratio test, the series -8/5+32/25-128/125+... is convergent.

a) There are 6 sides, one of them having 6 on it. Therefore, the chances is 1/6.

b) Rolling a six or not rolling a six is guaranteed, because there is no other option. The probability is 1.

c) There are 6 sides, five of them not having a 6. So, the probability is 5/6.

Answer:

Your answer is 2/1. 2 donuts every minute.

Step-by-step explanation: The rate you are given is 30 donuts every 30 minutes. This equals 30/15.

To make a unit rate, you must make the fraction have a ratio of x/1. You can simply do this by dividing and/or simplifying the equation 30/15.

The unit rate at which the bakery makes donuts is 2 donuts per minute. This is determined by dividing the total number of donuts (30) by the total time in minutes (15).

The question is asking for the unit rate at which the bakery makes donuts. A unit rate is a ratio that compares the quantity of one thing to 1 of something else. In this case, we want to find how many donuts the bakery makes in 1 minute. Given that the bakery can make 30 donuts every 15 minutes, we divide 30 (donuts) by 15 (minutes) to find the unit rate. So, 30 donuts ÷ 15 minutes = 2 donuts per minute. Therefore, the unit rate at which the bakery makes donuts is 2 donuts per minute.

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A = x = 110 degrees

B = 117 degrees

C = y = 63 degrees

D = 70 degrees

In a trapezoid, the two angles on the same side of the parallel lines are supplementary, meaning their measures add up to 180 degrees.

So, for angle A and angle D:

A + D = 180

x + 70 = 180

x = 180 - 70

x = 110

For angle B and angle C:

B + C = 180

117 + y = 180

y = 180 - 117

y = 63

Therefore, in the trapezoid ABCD:

A = x = 110 degrees

B = 117 degrees

C = y = 63 degrees

D = 70 degrees

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Answer:

Step-by-step explanation:

Total Number of Rolls = 10

Number of Defective Rolls = 3

Probability = Number of Defective Rolls / Total Number of Rolls

Probability = 3 / 10

Now there is one less defective roll.

Total Number of Rolls = 10 - 1

Number of Defective Rolls = 3 - 1

Total Number of Rolls = 9

Number of Defective Rolls = 2

Probability = Number of Defective Rolls / Total Number of Rolls

Probability = 2 / 9

Multiply the two probabilities together to find the overall probability.

3 / 10 * 2 / 9

3 * 2  = 6

10 * 9 = 90

6 / 90

Simplify

6 / 90 = 3 / 45 = 1 / 15 = 0.06666666666....

To find the probability of selecting two defective rolls of film in a row from a box of 10 rolls where 3 are defective, you multiply the probability of each selection. The result is a 1/15 chance of selecting two defective rolls consecutively.

The question deals with the concept of probability without replacement. In this scenario, we calculate the probability by considering each step independently. Initially, there are 10 rolls of film, and 3 are defective. The probability of selecting a defective roll first is 3 out of 10, or 3/10. Once a defective roll has been selected, there are now 9 rolls left with 2 being defective. The probability of selecting another defective roll is then 2 out of 9, or 2/9. To find the overall probability of both events happening in sequence ('and' probability), we multiply the probabilities of each step:

P(First defective and second defective) = P(First defective) * P(Second defective | First defective) = (3/10) * (2/9) = 6/90 = 1/15.

Therefore, the probability of selecting two defective rolls in a row is 1/15.

Hence zeros of function are
,x=-9, x=-8

Value of x that makes function value 0.

[tex]x^{2[/tex] +17x+72=0

[tex]x^{2}[/tex]+ 8x+9x+72=0

x(x+8)+9(x+8)=0

(x+9)(x+8)=0

x=-9,-8

Hence ,x=-9, x=-8

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Final answer:

The zeros of the function f(x) = x² + 17x + 72 are -9 and -8, found by factoring the quadratic equation.

Explanation:

To find the zeros of the function f(x) = x² + 17x + 72, we need to solve the equation for x when f(x) = 0. This can be done by factoring the quadratic equation if possible.

The quadratic factors as (x + 9)(x + 8) = 0. So the solutions to the equation x² + 17x + 72 = 0 are:

x = -9

x = -8

Therefore, the zeros of the function are -9 and -8.

Answer:

The selling price is $21

Step-by-step explanation:

What is the markup

Take the original price and multiply by the markup percent

markup = 15*40%

             = 15*.4

              = 6

The new price is the original price plus the markup

new price = 15+6

new price = 21

The selling price is $21

Answer:

45 units ^2

Step-by-step explanation:

make sure to divide the triangle and sqaure up when finding the area of this polygon..

hope this helps!!

Answer:

[tex]7.30\ mi[/tex]

Step-by-step explanation:

Let

b-----> the base of the missing measurement of the parallelogram

we know that

The area of the parallelogram is equal to

[tex]A=bh[/tex]

we have

[tex]A=27\ mi^{2}[/tex]

so

[tex]27=bh[/tex] ------> equation A

In this problem

[tex]h=3.7\ mi[/tex]

substitute the value in the equation A and solve for b

[tex]27=b(3.7)[/tex]

[tex]b=27/3.7=7.30\ mi[/tex]

Answer:

The area of rectangle is [tex]72\ units^{2}[/tex]

Step-by-step explanation:

see the attached figure with letters to better understand the problem

Let

[tex]A(3.10),B(12,1),C(16,5),D(7,14)[/tex]

we know that

The area of rectangle is equal to

[tex]A=(AB)(BC)[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Find the distance AB

we have

[tex]A(3.10),B(12,1)[/tex]

substitute in the formula

[tex]AB=\sqrt{(1-10)^{2}+(12-3)^{2}}[/tex]

[tex]AB=\sqrt{(-9)^{2}+(9)^{2}}[/tex]

[tex]AB=\sqrt{162}\ units[/tex]

Find the distance BC

we have

[tex]B(12,1),C(16,5[/tex]

substitute in the formula

[tex]BC=\sqrt{(5-1)^{2}+(16-12)^{2}}[/tex]

[tex]BC=\sqrt{(4)^{2}+(4)^{2}}[/tex]

[tex]BC=\sqrt{32}\ units[/tex]

Find the area of rectangle

[tex]A=(\sqrt{162})*(\sqrt{32})=72\ units^{2}[/tex]

Answer:

d is the answer

Step-by-step explanation:

Capacity of the fish tank is 40 gallons

The dot product is a scalar product, so you can eliminate the first two choices right away.

We have

[tex]v\cdot w=\langle3,4,7\rangle\cdot\langle6,-9,7\rangle=3\cdot6+4\cdot(-9)+7\cdot7=31[/tex]

Answer:

31

Step-by-step explanation:

v ⋅ w = (3)(6) + (4)(-9) + (7)(7)

v ⋅ w = 18 - 36 + 49

v ⋅ w = 31

Answer:

The length of the container is [tex]14\ in[/tex]

Step-by-step explanation:

we know that

The surface area of a triangular prism (a mailing container) is equal to

[tex]SA=2B+PL[/tex]

where

B is the area of the triangular base

P is the perimeter of the triangular base

L is the length of the container

step 1

Find the area of the base B

[tex]B=\frac{1}{2}(2)(1.7)=1.7\ in^{2}[/tex]

step 2

Find the perimeter of the base P

[tex]P=3(2)=6\ in[/tex]

step 3

Find the length L of the container

we have

[tex]SA=87.4\ in^{2}[/tex]

[tex]B=1.7\ in^{2}[/tex]

[tex]P=6\ in[/tex]

substitute and solve for L

[tex]87.4=2(1.7)+(6)L[/tex]

[tex]L=[87.4-2(1.7)]/(6)[/tex]

[tex]L=14\ in[/tex]

➷ Angles in a triangle total to 108 degrees

180 - (45 + 15) = 120

Angle B is 120 degrees.

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

The correct option is D.

Step-by-step explanation:

From the given figure it is clear that the measure of angle A is 45° and the measure of angle C is 15°.

According to the angle sum property of triangles, the sum of interior angles of a triangle is 180°. It means in triangle ABC,

[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]

[tex]45^{\circ}+\angle B+15^{\circ}=180^{\circ}[/tex]

[tex]\angle B+60^{\circ}=180^{\circ}[/tex]

[tex]\angle B=180^{\circ}-60^{\circ}[/tex]

[tex]\angle B=120^{\circ}[/tex]

The measure of angle B is 120°. Therefore the correct option is D.

Answer:

Set of all real numbers

Step-by-step explanation:

Given in the question the equation:

f(x) = ∛(x)

The domain of a cube root function is the set of all real numbers.

The interval notation (-∞ , ∞)

Cube Root of negative numbers exists:

Negative numbers can't have real number square roots, but negative numbers can have real number cube roots because when you are multiplying an odd number of negative numbers, the result is negative.

Example

(-2)³ = (-2)(-2)(-2) = -8

Answer:

[tex]\$20[/tex]

Step-by-step explanation:

Let

x-----> the cost of his lunch

y----> the cost of his dinner

we know that

[tex]x+y=872-136-210-500[/tex]

[tex]x+y=26[/tex] -----> equation A

[tex]x=0.3y[/tex] ---> equation B

substitute equation B in equation A

[tex]0.3y+y=26[/tex]

[tex]1.3y=26[/tex]

[tex]y=\$20[/tex] -----> the cost of the dinner

Answer:

  5/9

Step-by-step explanation:

The scale factor by which T was dilated is ...

   (side of T')/(corresponding side of T)

   = 20/36 = 10/18 = 5/9 . . . (reduced form)

Answer:

C) the answer is 5/9 or C

Step-by-step explanation:

i got it roght on the edgen quiz.

Step-by-step explanation:

We transform the system of equations to the form:

[tex]\left\{\begin{array}{ccc}ax+by=c\\dx+ey=f\end{array}\right[/tex]

Where a & b and d & e are relatively prime number.

If a ≠ d or b ≠ e then the system of equations has one solution.

Example:

[tex]\left\{\begin{array}{ccc}2x-3y=-4\\3x+3y=9\end{array}\right[/tex]

Add both sides of equations:

[tex]5x=5[/tex]     divide both sides by 5

[tex]x=1[/tex]

Substitute it to the second equation:

[tex]3(1)+3y=9[/tex]

[tex]3+3y=9[/tex]           subtract 3 from both sides

[tex]3y=6[/tex]       divide both sides by 3

[tex]y=2[/tex]

[tex]\boxed{x=1,\ y=2\to(1,\ 2)}[/tex]

If a = d and b = e and c = f then the system of equations has infinitely many solutions.

Example:

[tex]\left\{\begin{array}{ccc}2x+3y=5\\2x+3y=5\end{array}\right[/tex]

Change the signs in the second equation. Next add both sides of equations:

[tex]\underline{+\left\{\begin{array}{ccc}2x+3y=5\\-2x-3y=-5\end{array}\right}\\.\qquad0=0\qquad\bold{TRUE}[/tex]

[tex]\boxed{x\in\mathbb{R},\ y=\dfrac{5-2x}{3}}[/tex]

If  a = d and b = e and c ≠ f then the system of equations has no solution.

Example:

[tex]\left\{\begin{array}{ccc}3x+2y=6\\3x+2y=1\end{array}\right[/tex]

Change the signs in the second equation. Next add both sides of equations:

[tex]\underline{+\left\{\begin{array}{ccc}3x+2y=6\\-3x-2y=-1\end{array}\right}\\.\qquad0=5\qquad\bold{FALSE}[/tex]

Answer:

a) There is a 66.7% chance that you were given box 1

b) There is a 80% chance that you were given box 1

Step-by-step explanation:

To find this, we need to note that there is a 1/10 chance of getting a defective bulb with box 1 and a 1/20 chance in box 2.

a) To find the answer to this, find the probability of getting a defective bulb for each box. Since there is only one bulb pulled in this example, we just use the base numbers given.

Box 1 = 1/10

Box 2 = 1/2

From this we can see that Box 1 is twice as likely that you get a defective bulb. As a result, the percentage chance would be 2/3 or 66.7%

b) For this answer, we need to square each of the probabilities in order to get the probability of getting a defective one twice.

Box 1 = 1/10^2 = 1/100

Box 2 = 1/20^2 = 1/400

As a result, Box 1 is four times more likely. This means that it would be a 4/5 chance and have a probability of 80%

The solution involves using conditional probability and Bayes' theorem to find the chance of picking a defective lightbulb from a specific box. In part (b), the problem is slightly more complex, assuming the lightbulbs are selected independently.

This problem involves conditional probability. We're given two scenarios (a box is selected randomly, a lightbulb picked is defective, and two lightbulbs chosen are wrong). Let's use the following symbols: B1 (Box 1), B2 (Box 2), D (faulty lightbulb).

(a) The probability of a lightbulb being defective, given it came from Box 1 (P(D|B1)), is 0.10. The total likelihood of a lightbulb being inferior (P(D)) can be worked out from the total of defective lightbulbs divided by the total number of lightbulbs. The probability we're after, according to Bayes' theorem, is P(B1|D) = [P(D|B1)*P(B1)] / P(D).

(b) This question is more complex but can be solved similarly. Assuming the lightbulbs are selected independently, the probability of picking two defective lights from a given box is simply the square of picking one defective lightbulb from that box. Thus, we calculate P(2D|B1) = [P(D|B1)]^2 = (0.10)^2 = 0.01 (or 1%). Then, we use Bayes' theorem in part (a) to find P(B1|2D).

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Answer:

B. triangular pyramid.

Step-by-step explanation:

-Octahedron has eight faces that are equilateral  triangles, six vertices and twelve edges.

-Triangular pyramid has four triangular faces that have congruent isosceles triangles in which one of them is considered the base.

-Right triangular pyramid has a triangle base, three faces and six edges and the line that is located between the centre of the base and the vertex is perpendicular to the base.

-Regular rectangular prism has twelve sides, 8 vertices and six rectangular faces.

According to this, the answer is triangular pyramid.

Answer:

The answer is $6

Step-by-step explanation:

20 divided by 30% is 6! So it’s therefore 6$

Answer:

The answer is Ф = 1.82 or 4.46 ⇒ answer (c)

Step-by-step explanation:

* The domain of the function is 0 ≤ Ф ≤ 2π

- Lets revise the ASTC rule to solve the problem

# In the 1st quadrant all trigonometry functions are +ve

# In the 2nd quadrant sinФ and cscФ only are +ve

# In the 3nd quadrant tanФ and cotФ only are +ve

# In the 4th quadrant cosФ and secФ only are +ve

* Lets solve the problem

∵ secФ = -4.0545 ⇒ negative value

∴ Angle Ф is in the 2nd or 3rd quadrant

- In the 2nd quadrant Ф = π - α ⇒ (1)

- In the 3rd quadrant Ф = π + α ⇒ (2)

where α is an acute angle

* Now use the calculator to find α with radiant mode

- Let secα = 4.0545

∴ cosα = 1/4.0545

∴ α = cos^-1(1/4.0545) = 1.321585

* Substitute the value of α in (1) and (2)

∴ Ф = π - 1.321585 = 1.82

∴ Ф = π + 1.321585 = 4.46

* The answer is Ф = 1.82 or 4.46

Step-by-step explanation:

x^2 - 8x = 20

1. Subtract 20 from both sides

x^2 - 8x - 20 = 20 - 20

2. Simplify

x^2 - 8x - 20 = 0

3. Factor the equation out by grouping

(x - 10)(x + 2) = 0

4. Change signs:

x = 10, x = -2

Hope This Helped!!

~Shane

Answer:{-2,10}

Step-by-step explanation:

trust

The answer to your question is a. TRUE

Final answer:

The statement that the probability of a Type II error is represented by the Greek symbol β is true. The β symbol denotes the likelihood of failing to reject a false null hypothesis, while the power of a test (1-β) indicates the probability of accurately detecting a false null hypothesis.

Explanation:

The question is asking whether the statement 'The probability of a type ii error is represented by the greek symbol, β' is true or false. The correct answer is a. True. In statistics, a Type II error, which occurs when a false null hypothesis is not rejected, is indeed represented by the Greek letter β (beta). Therefore, the probability of committing a Type II error is denoted as β (beta). Conversely, a Type I error, symbolized by α (alpha), happens when the null hypothesis is incorrectly rejected. It is important to minimize both α and β as they represent the probabilities of these two types of errors. While α is often set by the researcher (commonly at 0.05), β is affected by factors such as effect size, sample size, and the chosen significance level α.

The power of a statistical test, defined as 1 - β, is the probability of correctly rejecting a false null hypothesis. A high statistical power is desirable as it indicates a lower chance of committing a Type II error. Estimating or calculating β directly can be complex, but understanding its role is crucial for interpreting the results of hypothesis testing.

[tex] \cot(x) \sin(x) = \frac{ \cos(x) }{ \sin(x) } \sin(x) = \cos(x) \\ \Rightarrow b. \cot(x) = \frac{ \cos(x) }{ \sin(x) } [/tex]

Answer:

B

Step-by-step explanation:

Answer:

The surface area of the cube is [tex]288\ units^{2}[/tex]

Step-by-step explanation:

we know that

The length of a diagonal of a cube is equal to

[tex]D=b\sqrt{3}[/tex]

where

b is the length side of a cube

In this problem we have

[tex]D=12\ units[/tex]

so

[tex]12=b\sqrt{3}[/tex]

solve for b

[tex]b=\frac{12}{\sqrt{3}}\ units[/tex]

Simplify

[tex]b=4\sqrt{3}\ units[/tex]

Find the surface area of the cube

The surface area of the cube is equal to

[tex]SA=6b^{2}[/tex]

substitute the value of b

[tex]SA=6(4\sqrt{3})^{2}=288\ units^{2}[/tex]

Answer:

the answer is D according to what i got

~batmans wife

Answer:

E. b/3 + 3

Step-by-step explanation:

For all real number b and c, if the product of c and 3 is b,

mathematically; 3c = b...(1)

To find the sum of c and 3 in terms of b;

Mathematically, the sum of c and 3 gives c+3...(2)

From equation 1, c = b/3

Substituting c = b/3 into equation 2, we will have;

(b/3) + 3 option E

= (b+9)/3

X=1/2

Explanation

Multiple both sides times 5

Then the 5 just cancels out on the left side and you’re left with 1/2