Suppose that, as course instructor, you decide instead that you want to calculate a 95% confidence interval for the population proportion of all Cal Poly students who have ever marched in a Memorial Day Parade, and that you would like the margin of error of your 95% confidence interval to be .05, and that you would like to use a (most) conservative sample size for this task. What sample size should you use

Answer:

p = 8

Step-by-step explanation:

Divide -5 to both sides

-5p = -40

5p = 40

p = 8

So p = 8

The total area of the garden is 52 ft².

First we need to calculate the area of the current garden and the area of the rectangular piece that will be added, and then add them together.

The current garden has an area of 20 square feet.

To find the area of the rectangular piece that will be added, we can use the formula for the area of a rectangle:

Area = length x width

The length of the rectangle is the distance between the points (-18, 13) and (-14, 13), which is 4 units. The width of the rectangle is the distance between the points (-18, 13) and (-18, 5), which is 8 units.

Therefore, the area of the rectangular piece that will be added is:

Area = 4 x 8 = 32 square feet

The total area of the garden is the sum of the areas of the current garden and the rectangular piece that will be added:

Total area = 20 + 32 = 52 square feet

Therefore, the total area of the garden is 52 ft².

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The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

\($\frac{AB}{BC} = \frac{AD}{AB}$\)

Cross-multiplying, we get:

\($AB^2 = BC \cdot AD$\)

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

\($\frac{AC}{BC} = \frac{AD}{AC}$\)

Cross-multiplying, we have:

\($AC^2 = BC \cdot AD$\)

Now, we can substitute the derived expressions into the original equation:

\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)

It was made possible by cross-product property.

Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

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Answer:

The length of the three sides \(5, \sqrt{58} , \sqrt{65}\)

The triangle is not a right triangle

Step-by-step explanation:

A = (3, 2) , B = ( 6, 9) , C = (10, 6)

Find the lengths using distance formula.

\(distance = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2}\)

\(AB = \sqrt{(6-3)^2 + (9-2)^2} = \sqrt{9 + 49 } = \sqrt{58}\)

\(BC = \sqrt{(10-6)^2 + (6-9)^2} = \sqrt{16 + 9} = \sqrt{25} = 5\)

\(AC = \sqrt{(3-10)^2+(2-6)^2} = \sqrt{49 + 16} = \sqrt{65}\)

Using Pythagoras theorem :

\((Longer \ side)^2 = sum \ of \ square \ of \ two \ other \ sides\)

Longest side is AC . So we will check if it satisfies Pythagoras theorem :

\(\sqrt{65} = \sqrt{58} + 5^2\\65 = 58 + 25\\\)

65 ≠ 58 + 25

So the sides does not satisfy Pythagoras theorem. Hence the triangle is not a right triangle.

Answer:

A. y = 2.5(2)^x

Step-by-step explanation:

Given that when

x = 1, f(x) =  5

x = 2, f(x) =  10

x = 3, f(x) =  20

x = 4, f(x) =  40

x = 5, f(x) =  80

x = 6, f(x) =  160

Considering all the options

y = 2.5(2)^x

Substitute x = 1

y = 2.5(2)^1 = 2.5 *2 = 5

Substitute x = 2

y = 2.5(2)^2 = 2.5 * 4 = 10

Substitute x = 3

y = 2.5(2)^3 = 2.5 * 8 = 20

Substitute x = 6

y = 2.5 (2)^6

= 2.5 * 64

= 160

Since the function is true for all the values of x substituted, then the answer is A. y = 2.5(2)^x

Answer:

It should be the first one (2)

Answer:

.

Step-by-step explanation:

.

The option that is a representation that shows y as a function of x is the graph in option 2. The answer is B.

A function is any relation or table of values which may be represented in a graph that has only one possible y value that is assigned to each x-value.

The first option is not a function because x-value 0 has two corresponding y-values, 4 and 9.

In the third option, we also have two y-values, 5 and -5, that is assigned to one x-value, 0. So, it is not a function.

The graph in option 2 represents y as a function of x, because no two y-values is assigned to the same x-value.

The answer is: B.

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The features related to vectors are listed below:

Case A: u' = (- 4√41 / 41, - 5√41/ 41)

Case B: Tip coordinantes of vector v: (x, y) = (10, 10)

Case C: r = 11.402

In this question we must determine three features related to vectors: (a) unit vector, (b) the definition of a vector based on the coordinates of its base and its tip, (c) The magnitude of a resulting vector.

Case A - Unit vector

Unit vectors are vectors with magnitude 1, for the case of vector u we have the following definition:

u' = u / ||u||

Where:

Please notice that the magnitude of the vector is determined by Pythagorean theorem:

r = √[(Δx)² + (Δy)²]

Where:

Thus, the unit vector of u is:

u' = (- 4, - 5) / √[(- 4)² + (- 5)²]

u' = (- 4, - 5) / √41

u' = (- 4 / √41, - 5 / √41)

u' = (- 4√41 / 41, - 5√41/ 41)

Case B - Definition of a vector

This can be found easily by vector subtraction:

v = Tip coordinates - Base coordinates

(3, 4) = (x, y) - (7, 6)

(x, y) = (3, 4) + (7, 6)

(x, y) = (10, 10)

Case C - Magnitude of a vector

The magnitude is found by means of Pyhtagorean theorem:

r = √[(- 4 - 3)² + (- 5 - 4)²]

r = √[(- 7)² + (- 9)²]

r = 11.402

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Answer:

5 = $ 5.25.    10= $ 6.50.   20= $9.00

Step-by-step explanation:

if this is wrong you can completely write me a really rude email or message or something

Answer:

40

Step-by-step explanation:

I believe that should be right

The probabilities are

i. P(male) ≈ 0.503

ii. P(hybrid) ≈ 0.324

iii. P(hybrid|male) ≈ 0.208

iv. P(hybrid|female) ≈ 0.441

v. P(female|hybrid) ≈ 0.677

P(hybrid|male) and P(male|hybrid) are not equal because the sample may not be representative of the entire population.

What is probability?

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.

a.

i. P(male) = number of males in the sample / total number in the sample = 154 / 306 ≈ 0.503

ii. P(hybrid) = number of hybrid cars purchased / total number in the sample = 99 / 306 ≈ 0.324

iii. P(hybrid|male) = number of males who purchased a hybrid / total number of males in the sample = 32 / 154 ≈ 0.208

iv. P(hybrid|female) = number of females who purchased a hybrid / total number of females in the sample = 67 / 152 ≈ 0.441

v. P(female|hybrid) = number of females who purchased a hybrid / total number of people who purchased a hybrid = 67 / 99 ≈ 0.677

b.

i. P(male) represents the probability of randomly selecting a male from the sample of 306 people who purchased a Honda Civic.

ii. P(hybrid) represents the probability of randomly selecting a car from the sample that has a hybrid engine.

iii. P(hybrid|male) represents the probability of selecting a hybrid car given that the person selected is male.

iv. P(hybrid|female) represents the probability of selecting a hybrid car given that the person selected is female.

v. P(female|hybrid) represents the probability of selecting a female given that the car selected has a hybrid engine.

c. No, P(hybrid|male) and P(male|hybrid) are not equal. P(hybrid|male) represents the probability of selecting a hybrid car given that the person selected is male, while P(male|hybrid) represents the probability of selecting a male given that the car selected has a hybrid engine. These probabilities are different because the sample is not necessarily representative of the entire population.

Hence, the probabilities are

i. P(male) ≈ 0.503

ii. P(hybrid) ≈ 0.324

iii. P(hybrid|male) ≈ 0.208

iv. P(hybrid|female) ≈ 0.441

v. P(female|hybrid) ≈ 0.677

P(hybrid|male) and P(male|hybrid) are not equal because the sample may not be representative of the entire population.

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Answer:

  (c)  neither

Step-by-step explanation:

A Hamiltonian Path visits every node once. A Hamiltonian Circuit is a loop that visits every node once.

__

This graph cannot have a Hamiltonian Circuit, because it has a node with degree 1. It cannot be part of a loop.

The graph cannot have either a Hamiltonian Path or Circuit, because the nodes in the two triangles cannot all be visited only once. Getting into and out of the triangle requires visiting a node twice.

This graph has neither a path nor a circuit.

The missing side is 30.

Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.

A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.

Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.

Assume that the missing side is x.

So that side ratio in similar triangle are equal;

14/20 = 21/x

So, x = 30.

Therefore, the missing side x is 30

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Triangle Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. According to the question the missing side is 30.

Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices. A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.

Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.
Assume that the missing side is x.
So that side ratio in similar triangle are equal;
14/20 = 21/x

So, x = 30.
Therefore, the missing side x is 30

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Answer:

Thus, the equation of line for point (-1, 2)  is y = x + 3.

Step-by-step explanation:

Answer:

The equation of the line is y = x + 3.

Step-by-step explanation:

A line that is parallel to y=x+4 and passes through the point (-1,2) will have the same slope as y=x+4. The slope of y=x+4 is 1, so the equation of the line will be in the form y = mx + b, where m=1. To find b, we can plug in x = -1 and y = 2 into the equation and solve for b.

y = mx + b

y = 1 * -1 + b

y = -1 + b

b = y + 1

b = 2 + 1

b = 3

The correct option is (a) ŷ = -1.34x+21.5 , that is the best model to fit the scatter plot.

A scatter plot (or scatter chart, scatter graph) uses dots to represent values for two(2) different numeric variables. The position of each dot on horizontal and vertical axis indicates values for an individual data point.

The model of the equation best for the plot is,

ŷ = -1.34x+21.5

At point (1,20),

ŷ  = -1.34x+21.5

20 = (-1.34 ×  1) + 21.5

20 ≈ 20.15

At point (3,19),

ŷ = -1.34x+21.5

19 = (-1.34 × 3) + 21.5

19 ≈17.45

At point (5,15),

ŷ = -1.34x+21.5

15 = (-1.34 × 5) + 21.5

15 ≈ 14.75

The model ŷ = -1.34x+21.5   is giving the best estimation.

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Answer: passes a horizontal AND vertical line test✅; no repeating x values✅

Step-by-step explanation:

To pass a line test, the function must pass BOTH the horizontal and vertical line test. If it only passes one but not the other, is it NOT a function.

Lastly, it can be a function if it has repeating y values.

Answer:

All real numbers greater than -3

Step-by-step explanation:

The domain of a log is the baseline is greater than 0.

Set x + 3 greater than zero and solve

x + 3 > 0

x > -3

\(x^2 -8x-2=0\\\\x^2 -8x=2\\\\x^2 -8x+16=18\\\\(x-4)^2 =18\\\\x-4=\pm \sqrt{18}\\\\\boxed{x=4 \pm \sqrt{18}}\)

Answer:

15

Step-by-step explanation:

if one side is 9, another is C, based on the angle tilt would have to be 15.

Hope its helps.

Answer:

One shirt costs $7.50.

One pair of shorts cost $15.45

Step-by-step explanation:

The experimental probability of the next balloon sold being green is 4/15.

Probability is a crucial concept in the field of mathematics that is used to measure the likelihood of an event happening.

According to the information given, the number of green balloons sold is 20, and the total number of balloons sold is the sum of all the colors, which is:

20 + 17 + 12 + 19 + 7 = 75

Now we can use these numbers to calculate the experimental probability of a green balloon being sold:

Experimental probability of a green balloon being sold = Number of green balloons sold / Total number of balloons sold

Experimental probability of a green balloon being sold = 20 / 75

Experimental probability of a green balloon being sold = 4/15

This means that if we randomly select a balloon from the store, the likelihood of it being green is 4 out of 15 or approximately 0.27 or 27%.

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Answer:

4/15

Step-by-step explanation:

Answer:

i think hcf of

24 and 40 is 8.

Answer:

Answer B

Step-by-step explanation:

In 47,602, the six is in the hundreds place.

We can divide 100/10 to get what place value it should be in. This gives us the tens place.

Now, we can see which number has a six in the tens place: Answer B, because sixty is 6 * 10.

Answer:

640

Step-by-step explanation:

Answer:

2261.46

Step-by-step explanation:

51142% = 5114200

√ 5114200 = 2261.46

Answer:

1230

Step-by-step explanation:

Sum of integers from 1 to n:

(n)(n + 1)/2

Find the sum of integers from 1 to 50 and subtract the sum of integers from 1 to 9.

(50)(51)/2 - (9)(10)/2 = 1230

Answer:

1230

Step-by-step explanation:

Counting numbers, also known as natural numbers, are the set of positive integers starting from 1 and continuing indefinitely.

To find the sum of 41 counting numbers starting from 10, we can use sum of an arithmetic series formula.

\(\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{n}{2}[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}\)

We want to find the sum of 41 counting numbers, so n = 41.

The first term is 10, so a = 10.

The common difference between consecutive terms is 1, so d = 1.

Substitute these values into the formula and solve.

\(\begin{aligned}S_{41}&=\dfrac{41}{2}\left[2(10)+(41-1)(1)\right]\\\\&=\dfrac{41}{2}\left[20+(40)(1)\right]\\\\&=\dfrac{41}{2}\left[20+40\right]\\\\&=\dfrac{41}{2}\left[60\right]\\\\&=\dfrac{2460}{2}\\\\&=1230\end{aligned}\)

Therefore, the sum of the counting numbers from 10 to 50 is 1230.

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

Explanation:

We're told that "given that it is less than 8", so we only focus on these values {1,2,3,4,5,6,7}. There are B = 7 items in this set.

Of those, the set {1,2,3,4,5,6} are less than 7. There are A = 6 items in this set.

The probability we're after is A/B = 6/7 = 0.8571

Answer:

I just got this question in my book, and i already solved it. so just saying that i now the answer, it is 0.8571