Janice walks 2 kilometers every morning. how many meters does janice walk each day? a) 0.20 meters b) 20 meters c) 200 meters d) 2,000 meters

(A) If Two independent events, A and B, are such that P(A) = 0. 2 P(A U B) = 0. 8, then probability P(B) =  5/8.

The possibility of the result of any random event is referred to as probability. This term refers to determining how likely an event is to occur. What are the chances of getting a head when we toss a coin in the air, for instance? The quantity of outcomes depends on the response to this question. Here, the outcome could be either head or tail. Thus, there is a 50% chance that the result will be a head.

The probability serves as a gauge for the likelihood that an event will occur. It gauges how likely an event is to occur. The probability equation is given by;

P(E) = Number of Favourable Outcomes/Number of total outcomes

We know that

P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = P(A) + P(B) - P(A).P(B)

0.8 = 0.2 + P(B) - 0.2.P(B)

0.5 = P(B)  - 0.2.P(B)

0.5 = 0.8.P(B)

P(B) = 0.5/0.8

P(B) = 5/8

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The appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).

To find the appropriate test statistic for a 2-sample z-test for two proportions, we need to calculate the standard error and then use it to compute the z-score. The formula for the standard error is:

SE = sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)]

Where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.

In this case, we have the following values:

X1 = 24 (number of successes in sample 1)

n1 = 200 (sample size 1)

X2 = 17 (number of successes in sample 2)

n2 = 150 (sample size 2)

To calculate the sample proportions, we divide the number of successes by the respective sample sizes:

p1 = X1 / n1 = 24 / 200 = 0.12

p2 = X2 / n2 = 17 / 150 = 0.1133

Now, we can plug these values into the formula to calculate the standard error:

SE = sqrt[(0.12 * (1 - 0.12) / 200) + (0.1133 * (1 - 0.1133) / 150)]

SE ≈ 0.0319

Finally, the test statistic (z-score) is calculated by subtracting the two sample proportions and dividing by the standard error:

Z = (p1 - p2) / SE

Z = (0.12 - 0.1133) / 0.0319

Z ≈ 0.2103

Therefore, the appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).

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Answer: 10 cups of sugar

Step-by-step explanation:

Cups of sugar : Cups of flour

                    2 : 3

                    ? : 15

Cross multiply

3? = 15 × 2

3? = 30

Divide both sides by 3

? = 10

He needs 10 cups of sugar.

To show that λâ1 is an eigenvalue of aâ1, we need to show that there exists a nonzero vector y such that aâ1y = λâ1y.
Let's use the hint and suppose that a nonzero vector x satisfies ax = λx. Then we can multiply both sides of this equation by aâ1 on the left to get:
aâ1(ax) = aâ1(λx)
x = aâ1(λx)
λâ1x = aâ1x
So if we let y = x, we have aâ1y = aâ1x = λâ1x = λâ1y. And since we started with a nonzero x, we know that y is also nonzero.
Therefore, we have shown that λâ1 is an eigenvalue of aâ1, as required.

To show that λ^(-1) is an eigenvalue of A^(-1), we will use the hint provided. Suppose a nonzero vector x satisfies Ax = λx, where λ is an eigenvalue of the invertible matrix A.

Since A is invertible, A^(-1) exists. Now, we can multiply both sides of Ax = λx by A^(-1) on the left:
A^(-1)(Ax) = A^(-1)(λx)

Using the associative property of matrix multiplication, we have:
(A^(-1)A)x = λ(A^(-1)x)

As A^(-1)A is the identity matrix I, the equation becomes:

Ix = λ(A^(-1)x)

Since Ix = x, we have:

x = λ(A^(-1)x)

Now, we want to find the eigenvalue of A^(-1). To do this, we'll divide both sides of the equation by λ:

x/λ = A^(-1)x

Since x is a nonzero vector, we can rewrite the equation as:

A^(-1)x = λ^(-1)x

Here, we see that λ^(-1) is indeed an eigenvalue of A^(-1), as it satisfies the eigenvalue equation A^(-1)x = λ^(-1)x for the nonzero vector x.

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Answer:

1. not random

2. random

3. random

4. not random

5. random

Step-by-step explanation:

I'm pretty sure those are the answers.

(a) Using confidence interval, we can reject the null hypothesis. (b) Using p-value, we can reject the null hypothesis.

(a) Decision using confidence interval:

We have, Sample size(n) = 150, Sample mean = 18.86 pounds, Population standard deviation(σ) = 3.7 pounds, Population mean(μ) = 20.5 pounds, and Significance level(α) = 10% = 0.1

We want to test whether the mean amount is less than 20.5 pounds or not.

Null Hypothesis: H0 : µ ≥ 20.5

Alternate Hypothesis: Ha : µ < 20.5

As we have n > 30, we can use the z-test.

z = (x - µ) / (σ / √n) = (18.86 - 20.5) / (3.7 / √150) = -4.12

The left-tailed critical z value for 10% significance level is -1.28.

Since our test statistic (-4.12) is less than the critical value(-1.28), we can reject the null hypothesis. Hence we can conclude that the mean amount is less than 20.5 pounds at 10% level of significance.

(b) Decision using p-value:

We have, Sample size(n) = 150, Sample mean = 18.86 pounds, Population standard deviation(σ) = 3.7 pounds, Population mean(μ) = 20.5 pounds, Significance level(α) = 10% = 0.1

We want to test whether the mean amount is less than 20.5 pounds or not.

Null Hypothesis: H0 : µ ≥ 20.5

Alternate Hypothesis: Ha : µ < 20.5

As we have n > 30, we can use the z-test.

z = (x - µ) / (σ / √n) = (18.86 - 20.5) / (3.7 / √150) = -4.12

The p-value of our test is P(z < -4.12) ≈ 0.

Since the p-value is less than the significance level, we can reject the null hypothesis. Hence we can conclude that the mean amount is less than 20.5 pounds at 10% level of significance.

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Answer:

123 people

Step-by-step explanation:

60 + 36x ≤ 4500  x is  the number of people

36x ≤ 4440  Subtract 60 from both sides of the equation

x ≤ 123.333...  Divide both sides  by 36.

We cannot have a portion of a person, so we would round down to the next person which would be 123.

The slope for the graph of elevator g in each interval is given as follows:

The y-intercept is given as follows:

y = 4.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b.

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

The slope for each interval is given by the average rate of change, hence:

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Answer:

The m∠YXW is 125°.

Addition equation: m∠YXW = m∠YXZ + m∠ZXW = 85° + 40° = 125°

Step-by-step explanation:

To find the m∠YXW you would need to add the m∠YXZ and m∠ZXW together:

m∠YXW = m∠YXZ + m∠ZXW = 85° + 40° = 125°

Answer:

A,B

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

2/3+5/6x=9

5/6x=8 1/3

5/6x=25/3

5x=50

x=10

Answer:

23x10

Step-by-step explanation:

Its 23x10^3 because its basically because 10 times 10 is a 100 and 100x10 is 10000 and 11x104 will be like 1000 smth (calculate it if u want)

An expression that is equivalent to (3⁶/y⁻⁵)² is: D. 3¹²·y¹⁰.

In Mathematics, an exponent is a mathematical operation that is commonly used in conjunction with an expression, in order to raise a given quantity to the power of another.

Mathematically, an exponent can be modeled by this mathematical expression;

bⁿ

Where:

By applying the division and multiplication law of exponents for powers of the same base to the given expression, we would have the following simplified expression:

(3⁶/y⁻⁵)²

(3⁶/1/1/y⁵)²

(3⁶ × y⁵)²

3¹²·y¹⁰

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Top left.

Step-by-step explanation:

Definition of a rectangle:

A four sided figure with 90 degree angles. The opposing side pairs are congruent with each other. It's the equivalent of a modified, upgraded parallelogram.

Now, the square is the answer since it fits all of the criteria of the rectangle, with the addition of having four congruent sides.

The only shape that represents a rectangle is the shape located in the upper left side of the figure. A square is a rectangle with four sides of equal length.

Quadrilaterals are closed figures with four line segments and whose sum of internal angles equals 360°, rectangles are quadrilaterals with four internal right angles and squares are rectangles with four sides of equal length.

The only shape that represents a rectangle is the shape located in the upper left side of the figure. A square is a rectangle with four sides of equal length.

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Answer:

the answer I got was 12.5 cm

The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

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Answer:

B) 15m

Step-by-step explanation:

Pythagoras theory → a² + b² = c², where c is the hypotenuse or longest side.

Answer = 15m

Hope this helps!

Answer:

15m

Step-by-step explanation:

u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D

Answer:

A = 0.5, 4

B = -3, 0

C = -1, 1

Answer:

A = (0.5, 4)

B = (-3,0)

C = (-1, 1)

Step-by-step explanation:

You just need to find the x and y points. Remember that the number for x comes before the number for y.

Answer:

The answer is

\( \huge g(3) = - 3\)

Step-by-step explanation:

\(g(x)= -2x +3\)

To find g(3) , substitute the value of x that's 3 into g(x). That is for every x in f(x) , replace it with 3

We have

\(g(3) = - 2(3) + 3 \\ \: \: \: \: = - 6 + 3 \\ \)

We have the final answer as

\(g(3) = - 3\)

Hope this helps you

to get the equation of any straight line, we simply need two points off of it, so hmmm let's use say (-1 , -1.25) and (8 , -3.5)

\((\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1.25})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-3.5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3.5}-\stackrel{y1}{(-1.25)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-1)}}}\implies \cfrac{-3.5+1.25}{8+1}\implies \cfrac{-2.25}{9}\implies -\cfrac{~~ \frac{225}{100}~~}{\frac{9}{1}} \\\\\\ -\cfrac{225}{100}\cdot \cfrac{1}{9}\implies -\cfrac{9}{4}\cdot \cfrac{1}{9}\implies -\cfrac{1}{4}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1.25)}=\stackrel{m}{-\cfrac{1}{4}}(x-\stackrel{x_1}{(-1)}) \\\\\\ y+1.25=-\cfrac{1}{4}(x+1)\implies y+\cfrac{5}{4}=-\cfrac{1}{4}x-\cfrac{1}{4} \\\\\\ y=-\cfrac{1}{4}x-\cfrac{1}{4}-\cfrac{5}{4}\implies y=-\cfrac{1}{4}x-\cfrac{6}{4}\implies y=-\cfrac{1}{4}x-\cfrac{3}{2}\)

Answer: yes the answer is 2:5 it isn’t right in just saying sum things

Step-by-step explanation:

Answer:

no sorry

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

Cube root of 8/125

Graph fourth represents a function with direct variation and the equation of the graph will be y = kx option (D) is correct.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

It is given that:

The graph is shown in the pictures

As we know,

The proportional relationship can be defined as:

y ∝ x

y = kx

k is the constant of proportionality:

y = kx is the equation of the line which passes through the origin.

Graph four passes through origin.

Thus, graph fourth represents a function with direct variation and the equation of the graph will be y = kx option (D) is correct.

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Driving a personal car would be the most cost-effective mode of transportation for this commute, with a total daily cost of approximately $4.60 ($3.60 for gas + $1 for travel time).

Based on the given information, the most cost-effective mode of transportation for this commute would be to drive a personal car. Taking public transportation or carpooling may be more environmentally friendly options, but they may not save as much money as driving alone.

Assuming an average speed of 60 miles per hour on the highway, the commute would take approximately 20 minutes each way, or 40 minutes round-trip. This means the total cost of travel time for each workday would be $40 ($60/hour x 2/3 hour).

Using a cost calculator such as GasBuddy, we can estimate that the cost of driving 20 miles per day (round-trip) would be around $3.60 per day, assuming an average fuel efficiency of 25 miles per gallon and a gasoline price of $2.50 per gallon.

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Answer:

The largest number that divides 15 and 27 is 3

Step-by-step explanation:

15 = 3 x 5

27 = 3 x 3 x 3

Greatest Common Factor = 3

The vertices of any planar graph can be colored in no more than 6 colors without any two adjacent vertices sharing the same color.

To prove by induction that the vertices of any planar graph can be colored in no more than 6 colors with no two vertices connected by an edge sharing the same color, we will use the concept of the Four Color Theorem.

The Four Color Theorem states that any planar graph can be colored with no more than four colors in such a way that no two adjacent vertices have the same color.

However, we will extend this theorem to use six colors instead of four.

Base case:

For a planar graph with a single vertex, it can be colored with any color, so the statement holds true.

Inductive hypothesis:

Assume that for any planar graph with k vertices, it is possible to color the vertices with no more than six colors without any adjacent vertices having the same color.

Inductive :

Consider a planar graph with k+1 vertices. We remove one vertex, resulting in a subgraph with k vertices.

By the inductive hypothesis, we can color this subgraph with no more than six colors such that no two adjacent vertices share the same color.

Now, we add the removed vertex back into the graph. This vertex is connected to some number of vertices in the subgraph.

Since there are at most six colors used in the subgraph, we can choose a color that is different from the colors of the adjacent vertices.

Thus, we have colored the graph with k+1 vertices using no more than six colors, satisfying the condition that no two adjacent vertices share the same color.

By the principle of mathematical induction, we can conclude that the vertices of any planar graph can be colored with no more than six colors, ensuring that no two adjacent vertices share the same color.

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Answer: 36

Step-by-step explanation: Multiplication