construct a matrix whose column space contains 1 0 1 and 0 1 1 and whose nullspace contains 2 1 2 .

The required probability for the given event is given as 0.5.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

Given that,

The probability of a door being locked is 70% = 0.7

Total number of keys is 10.

The number of keys being carried is 2.

Thus, there can be two cases for getting through the door.

Case 1: The door is locked.

The probability to open the door by 1 key is 1/10.

Then, the probability to open the door by 2 keys is 2/10 = 1/5.

Case 2: The door is open.

In this case no keys are needed which means the chance of getting through is the probability of door not being locked which is given as,

1 - 0.7 = 0.3.

Now, the overall probability should consider both the cases as,

P(getting through the door) = P(Door is closed and keys open it)

+ P(The door is open)

= 0.3 + 1/5

= 0.3 + 0.2

= 0.5.

Hence, the probability to get through the door without returning for more keys is 0.5.

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Answer:

1.3/4 × 2/2 = 6/8

2.3/4 × 3/3 = 9/12

3.3/4 × 4/4 = 12 /16

4. 3/4 × 5/5 = 15/20

Answer:

\(\boxed{m \angle CAB =99^{\circ}}\)

Step-by-step explanation:

We can use the law of cosines to determine measure of ∠CAB

If a, b and c are the three sides of a triangle and C is the angle opposite side c then the law of cosines says
c² = a² + b² - 2ab cos(C)

Here we are asked to find m∠CAB

The side opposite ∠CAB is BC which is 23 cm long. This is c in the formula

The other two sides, a and b are 13 cm and 17 cm

Applying the formula, using C to represent m∠CAB

\(23^2=\:13^2+\:17^2-\:2\:\cdot 13\cdot 17\cdot \cos \left(C\right)\)

First switch sides:
\(13^2+17^2-2\cdot \:13\cdot \:17\cos \left(C\right)=23^2\)

\(\rightarrow 69+289-442\cos \left(C\right)=529\\\\\rightarrow 458 -4 42\cos \left(C\right) = 529\\\)

\(\rightarrow -442\cos \left(C\right) = 529-458\\\\\rightarrow -442\cos \left(C\right) = 71\\\\\)

\(\rightarrow \cos \left(C\right)=-\dfrac{71}{442}\\\\\rightarrow \cos \left(C\right) = - 0.16063\\\\\)

\(\rightarrow C = \cos^{-1} (-0.16063)\)

\(\rightarrow C = 99.2437^{\circ}\)

Rounded to the nearest integer, this would become

\(\rightarrow C = \boxed{99^{\circ}}\)

Given the equation:

-39 = 4w + 7(w-3)

Let's solve the equation for w.

To solve take the following steps.

• Step 1.

Apply distributive property

• Step 2.

Combine like terms

• Step 3.

Add 21 to both sides

Step 4.

Divide both sides by 11

ANSWER:

w = -1.63

Answer:

Step-by-step explanation:

4s + 2c = 23

3s + 5c = 32

System of equations?

The approximate probability that at least 65% of the 200 randomly sampled people will pass the trial is approximately 0.9251 or 92.51%

To calculate the approximate probability that at least 65% of the 200 randomly sampled people will pass the trial, we can use the binomial distribution and the cumulative distribution function (CDF).

In this case, the probability of success (passing the trial) is p = 0.6, and the sample size is n = 200.

We want to calculate P(X ≥ 0.65n), where X follows a binomial distribution with parameters n and p.

To approximate this probability, we can use a normal distribution approximation to the binomial distribution when both np and n(1-p) are greater than 5. In this case, np = 200 * 0.6 = 120 and n(1-p) = 200 * (1 - 0.6) = 80, so the conditions are satisfied.

We can use the z-score formula to standardize the value and then use the standard normal distribution table or a calculator to find the probability.

The z-score for 65% of 200 is:

z = (0.65n - np) / √np(1-p))

z = (0.65 * 200 - 120) /√(120 * 0.4)

z = 1.44

Looking up the probability corresponding to a z-score of 1.44in the standard normal distribution table, we find that the probability is approximately 0.0749.

However, we want the probability of at least 65% passing, so we need to subtract the probability of less than 65% passing from 1.

P(X ≥ 0.65n) = 1 - P(X < 0.65n)

P(X ≥ 0.65)  =1 - 0.0749

P(X ≥ 0.65) = 0.9251

P = 0.9251 or 92.51%

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Answer:

The equation of the desired line is thus y = 4

Step-by-step explanation:

A line parallel to y = 5 is a horizontal line.  The x-coordinate of every point on this line can take on any x-value; the y-coordinate is always 5.

The line that passes through the point (1, 4) has the constant y-coordinate 4, whereas x can take on any value.

The equation of the desired line is thus y = 4; this line passes through (1, 4) as required and is parallel to y = 5.

Answer:

The measure of angle WVX is 140°.

Step-by-step explanation:

Let x be the measure of angle WVX.

\( \frac{14}{9} \pi = 2x\)

\( x = \frac{7}{9} \pi( \frac{180}{\pi}) = 140 \: degrees\)

Answer:

angle = arc length/radius
in this case, the arc length is 14/9*\(\pi\) and the radius is 2. Upon multiplying these, you get 140.

so, the answer is 140 degrees.

Answer:

Father=36 years old

Step-by-step explanation:

5 people 4 children and a father

average age=12

add the ages

3+5+6+10=24

24+12=36

check the work

36 +24=60

60/5=12

answer=36

Answer:

36 years old

Step-by-step explanation:

The average age of father and four children can be expressed in mathematics as:

\(\displaystyle \large{\dfrac{f+c_1+c_2+c_3+c_4}{5}}\)

The above expression is what you call average value or mostly known as mean - the mean value is sum of all data values divided by number of data values. The formula reference for mean/average value is:

\(\displaystyle \large{\dfrac{x_1+x_2+x_3+...+x_n}{n} = \dfrac{1}{n} \sum_{i=1}^n x_i}\)

Determine or let the following be:

It is also given in the question that children’s ages are 3, 5, 6 and 10. Hence:

\(\displaystyle \large{\dfrac{f+3+5+6+10}{5} = 12}\)

From above, it is also given that average of father’s age and children’s age is 12 years old - that now gives us an equation. What we have to do now is to solve for f.

First, multiply 5 both sides to get rid of denominator.

\(\displaystyle \large{\dfrac{f+3+5+6+10}{5} \cdot 5 = 12 \cdot 5}\\\\\displaystyle \large{f+3+5+6+10=60}\)

Evaluate 3+5+6+10 which equals 24.

\(\displaystyle \large{f+24=60}\)

Next, subtract both sides by 24 to isolate f-term.

\(\displaystyle \large{f+24-24=60-24}\\\\\displaystyle \large{f=36}\)

Finally, we have received the value of term which is f = 36. We know that the term represents father’s age and therefore, father’s age is 36 years old!

If you have any doubts, please let me know in the comment!

The function \(f(x) = x^6e^(-x)\) is increasing on the interval (0, ∞), meaning that as x increases from 0 to infinity, the values of f(x) also increase.

To determine the interval on which f(x) is increasing, we need to find where the derivative of f(x) is positive. Let's start by finding the derivative of f(x):

\(f'(x) = d/dx (x^6e^(-x))\)

To find the derivative, we can use the product rule:

f'(x) = 6x^5e^(-x) - x^6e^(-x)

Now, we need to determine the sign of f'(x) to identify where f(x) is increasing. We can analyze the sign of f'(x) by examining the behavior of its factors: \(6x^5e^(-x) and -x^6e^(-x)\). The factor 6x^5e^(-x) is always positive for x > 0 since\(x^5\) and \(e^(-x)\) are positive for positive x. The factor\(-x^6e^(-x)\) is negative for x > 0 since x^6 is positive, and e^(-x) is positive for positive x. Since \(f'(x) = 6x^5e^(-x) - x^6e^(-x)\) is positive for x > 0, it means that f(x) is increasing on the interval (0, ∞).

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Answer:

The first option

Step-by-step explanation:

the sign only flips when there is a negative number.

i hope this is correct

The coefficient of determination (r-squared) provides an indication of how well the regression model fits the data and the value of r is  0.3574

In this example, the r-squared value is 12.78%, which means that 12.78% of the variation in verbal SAT scores can be explained by the variation in math SAT scores. The least squares regression equation is yhat = 383.3 + 0.3489x, where yhat is the predicted verbal score and x is the math score.

The coefficient of correlation (r) provides a measure of the strength of the linear relationship between two variables. In this example, the coefficient of correlation (r) can be calculated from the coefficient of determination (r-squared) as follows: r = √r-squared = √12.78% = 0.3574. This indicates that there is a weak linear relationship between verbal and math SAT scores.

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To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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Determine whether each data set is likely to be normally distributed. Here are my evaluations for each data set:

1. The number of eggs collected each day on a farm:
Yes, this data set is likely to be normally distributed. The daily egg collection should follow a bell-shaped curve, with an average number of eggs collected per day and a standard deviation accounting for variability.

2. The number of yolks in randomly selected eggs:
No, this data set is not likely to be normally distributed. The number of yolks in an egg is a discrete variable, with most eggs having only one yolk, and a few having two or more. This distribution would be skewed and not follow a normal distribution.

3. The weights of eggs in the kitchen of a restaurant:
Yes, this data set is likely to be normally distributed. The weights of eggs should follow a bell-shaped curve, with an average weight and a standard deviation accounting for variability.

4. The number of eggs in cartons sold at a supermarket:
No, this data set is not likely to be normally distributed. The number of eggs in a carton is a fixed, discrete variable (e.g., 6, 12, or 18 eggs). The distribution would be discrete and not follow a normal distribution.

Your answer: 1. Yes, 2. No, 3. Yes, 4. No

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Answer:

0.0084033613

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation is y=7x

x      y          Calculation

5     35         y=7x, y=7*5, y=35

6     42         y=7x, y=7*6, y=42

7      49       y=7x, y=7*7, y=49

8     56          y=7x, y=7*8, y=56

Answer:

x-3y-7=0

Step-by-step explanation:

Dont care bruuhh

Answer: 26

Step-by-step explanation:

Two Angles are Complementary when they add up to 90 degrees (a Right Angle). Then

∠A + ∠B = 90

∠A =90- ∠B

∠A  = 26

Answer:

The measure of \(\angle A\):

\(\angle A = 26\textdegree\)

Step-by-step explanation:

Since both \(\angle A\) and \(\angle B\) are complementary (Which they both add up to 90°), and you want to find the measure of

Measure of \(\angle A\): unknown

Measure of \(\angle B\): 64°

Finding the measure of \(\angle A\):

\(90 - 64 = 26\)

\(\angle A = 26\textdegree\)

So, the measure for \(\angle A\) is \(26\textdegree\).

Answer:

1.5

Step-by-step explanation:

Answer:

m=3/2

Step-by-step explanation:

To determine the sign of the sum of two integers when one integer is positive and the other is negative, we can follow a simple rule based on their magnitudes.

If the magnitude of the positive integer is greater than the magnitude of the negative integer, the sum will be positive. This is because the positive integer outweighs the negative integer, resulting in a positive value.

On the other hand, if the magnitude of the negative integer is greater than the magnitude of the positive integer, the sum will be negative. In this case, the negative integer dominates and determines the sign of the sum.

In both scenarios, the sign of the larger magnitude integer takes precedence and determines the sign of the sum. It is important to note that the sum will always have the sign of the integer with the larger magnitude, regardless of the specific values of the integers involved.

By considering the magnitudes of the integers, we can easily determine the sign of their sum when one integer is positive and the other is negative.

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The minimum wage set by the government at $7.50 per hour does not result in a pay cut for unskilled workers, as it is below the equilibrium wage of $8.00 per hour.

The wage rate remains unchanged, and the labor market remains in balance.

The statement is false.

False.

The equilibrium wage in the market for unskilled labor is $8.00 per hour, which means that the market naturally sets the wage rate at this level, based on the forces of supply and demand.

The government then sets a minimum wage at $7.50 per hour.

Since the minimum wage is below the equilibrium wage, it does not directly impact the wage rate for unskilled workers.
The equilibrium wage represents the point at which the supply of labor (the number of workers willing to work at a given wage) equals the demand for labor (the number of workers that employers are willing to hire at a given wage).

In this case, both workers and employers are satisfied with the $8.00 per hour wage, and the labor market is balanced.
The government sets a minimum wage below the equilibrium wage, it essentially sets a wage floor that is not binding. Employers are still willing to pay the equilibrium wage of $8.00 per hour, and workers are still willing to accept this wage.

The wage for unskilled workers remains at $8.00 per hour, and there is no pay cut of 50 cents per hour.

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The images of the given points after a counterclockwise rotation of 30° about the origin are approximately: A: (-0.69, -4.12), B: (3.64, -1.34), C: (-3.92, -1.70), D: (1.70, -3.47)

To find the image of the given points after a counterclockwise rotation of 30° about the origin, we can use the rotation matrix. The rotation matrix for a counterclockwise rotation of an angle θ is given by:

\[

\begin{bmatrix}

\cos(\theta) & -\sin(\theta) \\

\sin(\theta) & \cos(\theta)

\end{bmatrix}

\]

In our case, we want to rotate the points through 30° counterclockwise, so θ = 30°.

Let's go through each given point and apply the rotation matrix to find its image.

A = (-1.13, -3.96):

Using the rotation matrix, we have:

\[x' = \cos(30°) \cdot (-1.13) - \sin(30°) \cdot (-3.96)\]

\[y' = \sin(30°) \cdot (-1.13) + \cos(30°) \cdot (-3.96)\]

Calculating the values, we get:

\[x' \approx -0.69\]

\[y' \approx -4.12\]

Therefore, the image of A after a counterclockwise rotation of 30° is approximately (-0.69, -4.12).

B = (2.87, -2.96):

Using the rotation matrix, we have:

\[x' = \cos(30°) \cdot (2.87) - \sin(30°) \cdot (-2.96)\]

\[y' = \sin(30°) \cdot (2.87) + \cos(30°) \cdot (-2.96)\]

Calculating the values, we get:

\[x' \approx 3.64\]

\[y' \approx -1.34\]

Therefore, the image of B after a counterclockwise rotation of 30° is approximately (3.64, -1.34).

C = (-2.87, -2.96):

Using the rotation matrix, we have:

\[x' = \cos(30°) \cdot (-2.87) - \sin(30°) \cdot (-2.96)\]

\[y' = \sin(30°) \cdot (-2.87) + \cos(30°) \cdot (-2.96)\]

Calculating the values, we get:

\[x' \approx -3.92\]

\[y' \approx -1.70\]

Therefore, the image of C after a counterclockwise rotation of 30° is approximately (-3.92, -1.70).

D = (1.13, -3.96):

Using the rotation matrix, we have:

\[x' = \cos(30°) \cdot (1.13) - \sin(30°) \cdot (-3.96)\]

\[y' = \sin(30°) \cdot (1.13) + \cos(30°) \cdot (-3.96)\]

Calculating the values, we get:

\[x' \approx 1.70\]

\[y' \approx -3.47\]

Therefore, the image of D after a counterclockwise rotation of 30° is approximately (1.70, -3.47).

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Answer: natural; whole; integer; rational; real

Step-by-step explanation:

16/4=4

Natural: numbers that are greater than 0.

4 is greater than 0

Whole: numbers that are equal or greater than 0

4 is equal or greater than 0

Integer: numbers that have no decimal points

4 has no decimal points

Rational: numbers that can be written as fraction

4=16/4 which is fraction

It is already rational, so it will not be irrational.

Real: all number you can name are real number

4 is four

Without more information about the relationship between the sides or the length of the remaining side, we cannot determine the exact length of EF or the exact perimeter of triangle EFG.

Since triangle EFG is an isosceles triangle with EG = EF, the length of EF will be the same as the length of EG. Let's denote this length as x.

To find the approximate length of EF, we need more information about the triangle or the relationship between the sides. Without this information, we cannot determine the exact value of x or EF.

However, we can still calculate the approximate perimeter of triangle EFG. The perimeter of a triangle is the sum of the lengths of all its sides.

In this case, since triangle EFG is isosceles, we can consider that the perimeter is approximately 2 times the length of EF plus the length of the remaining side.

Let's denote the length of the remaining side as y. The approximate perimeter (P) can be calculated as P ≈ 2x + y.

Since we don't have the value of y, we cannot determine the exact perimeter. Therefore, we cannot select a specific answer option among the given choices.

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The series converges on the interval from 7 inclusive to 9 exclusive.

To find the radius of convergence, we use the ratio test:

So the series converges absolutely if |x - 8| < 1, and diverges if |x - 8| > 1. Therefore, the radius of convergence is R = 1.

To find the interval of convergence, we need to test the endpoints x = 7 and x = 9:

When x = 7, the series becomes:

[infinity] (-1)ⁿ (n+9) / (n+1)

n = 0

which is an alternating series that satisfies the conditions of the alternating series test. Therefore, it converges.

When x = 9, the series becomes:

[infinity] 1 / (n+1)

n = 0

which is a p-series with p = 1, which diverges.

Therefore, the interval of convergence is [7, 9).

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Passage:

Big Time Movers charges an initial fee of $24.50, plus $12.75 an hour for their moving services. On holidays, they charge 2.5 times their regular total amount.

Question:

If they made $188.75 on a job on New Year’s Day, how many hours did they work?

Answer:

Big Time Movers worked "4" hours on New Year’s Day.

Step-by-step explanation:

I did the instruction on edge 202 and got it right