22/24 Marks
51%
The diagram shows a star made by surrounding a
regular octagon with triangles.
Explain why angle a must be 135º.
+
I

Answer:

A sample of 17 must be selected.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.96}{2} = 0.02[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.02 = 0.98[/tex], so Z = 2.054.

Now, find the margin of error M as such

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

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The standard deviation from a previous study is 4 hours.

This means that [tex]\sigma = 4[/tex]

How large a sample must be selected if he wants to be 96% confident of finding whether the true mean differs from the sample mean by 2 hours?

A sample of n is required.

n is found for M = 2. So

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

[tex]2 = 2.054\frac{4}{\sqrt{n}}[/tex]

[tex]2\sqrt{n} = 2.054*4[/tex]

Simplifying both sides by 2:

[tex]\sqrt{n} = 2.054*2[/tex]

[tex](\sqrt{n})^2 = (2.054*2)^2[/tex]

[tex]n = 16.88[/tex]

Rounding up:

A sample of 17 must be selected.

Given:

After deduction of 4 paisa in a Rupee a sum of Rs 720 is left.

To find:

The original amount.

Solution:

We know that,

1 Rs. = 100 paisa

After deduction of 4 paisa in a Rupee, we get

[tex]100-4=96[/tex]

It means Rs. 720 is the 96% of the original amount.

Let x be the original amount.

[tex]720=\dfrac{96}{100}x[/tex]

[tex]72000=96x[/tex]

[tex]\dfrac{72000}{96}=x[/tex]

[tex]750=x[/tex]

Therefore, the original amount is Rs. 750.

If the slope of the line y = mx − 4 is  less than the slope of the line y = x − 4, this shows that m will be any values less than 1 i.e. m < 1. This gives a true statement

The slope of a line defines the steepness of such a line. It is the ratio of the rise to the run of a line.

The general formula for calculating an equation of a line is expressed as:

[tex]y = mx + b[/tex] where:

m is the slope of the line

Given the equation of the line, [tex]y=x-4[/tex] the slope of the line will be derived through comparison as shown:

[tex]mx=1x\\[/tex]

Divide through by x

[tex]\dfrac{mx}{x} = \dfrac{1x}{x}\\ m=1[/tex]

Hence the slope of the line y = x - 1 is 1.

According to the question, since we are told that the  slope of the line

y = mx − 4 is  less than the slope of the line y = x − 4, this shows that m will be any values less than 1 i.e. m < 1. This gives a true statement

Learn more about the slope of a line here: https://brainly.com/question/16949303

Answer:

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

4 + 2 + 5 + 4 + 0 + 1 + 1 + 3 = 20

Answer:

Step-by-step explanation:

Factor pairs:

1, 18

2, 9

3, 6

Answer:

[tex]\huge\boxed{\text{D)} \ 15x^4 + 2x^3 - 8x^2 - 22x - 15}[/tex]

Step-by-step explanation:

We can solve this multiplication of polynomials by understanding how to multiply these large terms.

To multiply two polynomials together, we must multiply each term by each term in the other polynomial. Each term should be multiplied by another one until it's multiplied by all of the terms in the other expression.

Let's first start by multiplying the first term of the first polynomial, [tex]3x^2[/tex], by all of the terms in the second polynomial. ([tex]5x^2+4x+5[/tex])

Now, we can add up all these expressions to get the first part of our polynomial. Ordering by exponent, our expression is now

Now let's do the same with the second term ([tex]-2x[/tex]) and the third term ([tex]-3[/tex]).

Phew, that's one big polynomial! We can simplify it by combining like terms. We can combine terms that share the same exponent and combine them via their coefficients.

This simplifies our expression down to [tex]15x^4 + 2x^3 - 8x^2 - 22x - 15[/tex].

Hope this helped!

Answer:

11/12

Step-by-step explanation:

1/4 + 2/3

= 3/12 + 8/12

= 11/12

Answer: hello your question is incomplete below is the complete question

The Two vectors;  A = 5i + 6j +7k and B = 3i -8j +2k.

answer;

angle = 102°

Step-by-step explanation:

multiplying the vectors

A.B = |A| * |B|* cosθ

hence : Cosθ = (Ai*Bi )+ (Aj*Bj) + ( Ak*Bk/ (√A^2 *√B^2 )

                       = 15 - 48 + 14 /(√25+26+29) * (√9+64+4)

                      = -0.206448454

θ = cos^-1 ( -0.206448454) = 101.9° ≈ 102°

Answer:

212.06

Step-by-step explanation:

can't really explain since the formula is fricking long but trust me that's uts 212.06 in²

The equation "a - 3x = 0" is correctly written because it follows the standard format of an algebraic equation.

Given that,

All the equations are,

1. a + 0.2x

2. 5b - 5x + 2

3. a - 3x = 0

Now, from equation ''a - 3x = 0'',

In this equation, the variable "a" subtracted from 3 times the variable "x" equals zero.

The equal sign (=) indicates that the expression on both sides of the equation is equivalent.

The equation is properly balanced and expresses equality between the two sides.

It accurately represents a relationship between the variables "a" and "x" where the value of "a" is dependent on the value of "x" in order to satisfy the equation.

So, The correctly written algebraic equation is:

a - 3x = 0

To learn more about the equation visit:

brainly.com/question/28871326

#SPJ4

Answer:

-6

Step-by-step explanation:

V = 6x + b

 1/2 V -3 x = -3

V - 6x = -6

V - 6x  =  b

Answer:

ab=14.4

Step-by-step explanation:

This is going to be tricky to explain over text, so try to bear with me :) You have the information given above. Let's start with just ad = 11.6 for now. since these are variables, it can also be understood be understood as a times d= 11.6.  Knowing this, we can figure out that d = 11.6/a, when you divide both sides by a. You now have d, so plug (11.6/a) into cd=6.7. You have to do the same thing you did last time, except this time you are aiming to get c by itself. So, multiply both sides by a/11.6 and you get c = (6.7a)/ 11.6.  Guess what, you know c now! so you put (6.7a)/11.6 in for c in the equation given to you earlier, bc =8.3. The math gets a bit messy here, but you basically solve for b here, which, when you crunch the numbers down, ends up being ~14.3705 divided by a. You are looking for ab, so just multiply both sides by a, and round to the nearest tenth so that you have ab= 14.4  

Answer:

0.2528 = 25.28% probability of selling no more than 2 properties in one week.

Step-by-step explanation:

For each property, there are only two possible outcomes. Either they are sold, or they are not. The chance of selling any one property is independent of selling another property, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A real estate agent has 12 properties that she shows.

This means that [tex]n = 12[/tex]

She feels that there is a 30% chance of selling any one property during a week.

This means that [tex]p = 0.3[/tex]

Compute the probability of selling no more than 2 properties in one week.

2 or less sold, which is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{12,0}.(0.3)^{0}.(0.7)^{12} = 0.0138[/tex]

[tex]P(X = 1) = C_{12,1}.(0.3)^{1}.(0.7)^{11} = 0.0712[/tex]

[tex]P(X = 2) = C_{12,2}.(0.3)^{2}.(0.7)^{10} = 0.1678[/tex]

Then

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0138 + 0.0712 + 0.1678 = 0.2528[/tex]

0.2528 = 25.28% probability of selling no more than 2 properties in one week.

Answer:

No se me puedes ayudar por fa

Answer:

8

Step-by-step explanation:

Create an expression to model the situation. One can do this by simply rewriting the written expression in terms of numbers and variables. Use the variable (x) to represent the unknown value.

[tex]5(x)=\frac{1}{3}(64+56)[/tex]

Simplify this expression,

[tex]5(x)=\frac{1}{3}(64+56)\\5x=\frac{1}{3}(120)\\5x=40\\[/tex]

Use inverse operations to solve for (x),

[tex]5x=40\\x=8[/tex]

Answer:

[tex]P(x < 3) = 25\%[/tex]

[tex]E(x) = 3[/tex]

Step-by-step explanation:

The given parameters can be represented as:

[tex]\begin{array}{ccccccc}x & {5} & {4} & {3} & {2} & {1}& {0} & P(x) & {25\%} & {30\%} & {20\%} & {15\%} & {5\%} & {5\%} \ \end{array}[/tex]

Solving (a): P(x < 3)

This is calculated as:

[tex]P(x < 3) = P(x = 0) + P(x = 1) + P(x =2)[/tex] ----- i.e. all probabilities less than 3

So, we have:

[tex]P(x < 3) = 5\% + 5\% + 15\%[/tex]

[tex]P(x < 3) = 25\%[/tex]

Solving (b): Expected number of events

This is calculated as:

[tex]E(x) = \sum x * P(x)[/tex]

So, we have:

[tex]E(x) = 5 * 25\% + 4 * 30\% + 3 * 20\% + 2 * 15\% + 1 * 5\% + 0 * 5\%[/tex]

[tex]E(x) = 125\% + 120\% + 60\% + 30\% + 5\% + 0\%[/tex]

[tex]E(x) = 340\%[/tex]

Express as decimal

[tex]E(x) = 3.40[/tex]

Approximate to the nearest integer

[tex]E(x) = 3[/tex]

Answer:

No, the sum of all the probabilities is not equal to 1.

Step-by-step explanation:

Given

[tex]\begin{array}{ccccc}x & {0} & {1} & {2} & {3} & {P(x)} & {0.001} & {0.007} & {0.033} & {0.059} \ \end{array}[/tex]

Required

Determine if the given parameter is a probability distribution

For a probability distribution to exist, the following must be true;

[tex]\sum P(x)=1[/tex]

So, we have:

[tex]\sum P(x) = 0.001 + 0.007 + 0.033 + 0.059[/tex]

[tex]\sum P(x) = 0.1[/tex]

Hence, it is not a probability distribution because the sum of all probabilities is not 1

Answer:

The 95% confidence interval for the proportion of students who work out 4 or more times a week is (0.2432, 0.3568).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

In a random sample of 250 students, we found that 75 work out 4 or more times a week.

This means that [tex]n = 250, \pi = \frac{75}{250} = 0.3[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 - 1.96\sqrt{\frac{0.3*0.7}{250}} = 0.2432[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 + 1.96\sqrt{\frac{0.3*0.7}{250}} = 0.3568[/tex]

The 95% confidence interval for the proportion of students who work out 4 or more times a week is (0.2432, 0.3568).

Answer:

$402.700 capital gain

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

x^3 = 125

Take the cubed root of each side

x^3 ^ (1/3) = 125 ^ (1/3)

x = 5

Answer:

Si se suman 3 trabajadores la producción será 5250 plumas.

Step-by-step explanation:

Inicialmente tenemos 6 trabajadores, al añadir 3 trabajadores más tendríamos ahora 9 trabajadores:

[tex] 6 + 3 = 9 [/tex]

Entonces, la producción de plumas (P) sería ahora:

[tex] P = \frac{3500}{6}*9 = 5250 [/tex]

Por lo tanto, si se suman 3 trabajadores la producción será 5250 plumas.

Espero que te sea de utilidad!                          

Answer:

Attached images

It was just easier for me this way.

Let me know in comments if you have questions.

Step-by-step explanation:

Answer:  13.2

In fraction form, this is 66/5

=============================================================

Explanation:

The five values are in the ratio 1:2:3:4:5 which scales up to 1x:2x:3x:4x:5x for some positive number x.

Add up the pieces of the second ratio and set that sum equal to 198. Then solve for x.

1x+2x+3x+4x+5x = 198

15x = 198

x = 198/15

x = 66/5

x = 13.2 is the smallest number since 1x = 1*13.2 = 13.2 was the smallest value of the ratio 1x:2x:3x:4x:5x.

Step-by-step explanation:

4/6

=2/3

That's what I could show you

Answer:

A

Step-by-step explanation:

Answer:

S = v1 t1 = 7 t1    traveling downstream

S = v2 t2 = 5 t2    traveling upstream

7 t1 = 5 t2

7 (6 - t2) = 5 t2     since t1 + t2 = 6

42 - 7 t2 = 5 t2

t2 = 42 / 12 = 3.5 hrs so t1 = 2.5 hrs

S = 7 t1 = 7 * 2.5 = 17.5 mi

Also, S = 5 t2 = 5 * 3.5 = 17.5 mi

Answer:

306 square meters.

Step-by-step explanation:

Divide the shape into 2 rectangles.

Lets do the one that is sticking to the top first.

The area is 6 * 15, which is 90.

Lets do the second rectangle. The area is:

27 * 8, which is 216.

Add them all up (90 + 216), which is 306.

Answer:

306m²

Step-by-step explanation:

Split the shape into two rectangles with the accureate lengths

The top-most of the two rectangles with length 6m and width 15m:

6 x 15 = 90 m² (area of rectangle A)

The bottom rectangle:

27(full length) x 8m(full width) = 216m²

Add the two areas together for the full shape

216 + 90 = 306m²

Answer: The Third Graph/ C

Step-by-step explanation: