How to solve it and the answer

The probability that the drawn bead will be blue is 1/3.

Given that,

A cloth sack contains 25 red beads, 75 green beads, and 50 blue beads.

Total number of beads in the sack = 25 + 75 + 50 = 150

Number of blue beads = 50

Probability of drawing a blue bead = Number of blue beads / Total number of beads

= 50/150

= 1/3

Hence the required probability of drawing blue bead is 1/3.

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Answer:

6log 2

Step-by-step explanation:

log 16 + log 4 = log 2⁴ + log 2² = 4log 2 + 2log 2 = 6log 2

Explanation:

The three lengths given are

Notice that a+b = 1 cm +3 cm = 4 cm which is NOT larger than c = 100 cm

Therefore, a triangle is NOT possible.

For more information, check out the triangle inequality theorem.

That theorem says "a triangle is possible if any two sides add to something larger than the third side.

The zeros of the function are x = 0, x = 7, and x = 9.

The graph of f(x) is concave down near x = 7 and concave up near x = 9.

We have,

To find the zeros of the function f(x) = x^4 - 16x^3 + 63x^2,

We need to set f(x) equal to zero and solve for x:

x^4 - 16x^3 + 63x^2 = 0

Factor out x^2:

x^2(x^2 - 16x + 63) = 0

Factor the quadratic term:

x^2(x - 7)(x - 9) = 0

So the zeros of the function are x = 0, x = 7, and x = 9.

To describe the behavior of the graph at each zero, we can use the first and second derivative tests.

The first derivative of f(x) is:

f'(x) = 4x^3 - 48x^2 + 126x

The second derivative of f(x) is:

f''(x) = 12x^2 - 96x + 126

At x = 0, we have a double root, since x = 0 is a zero of multiplicity 2.

From the first derivative test, we see that f'(x) changes sign from negative to positive at x = 0, indicating that f(x) has a local minimum at x = 0.

From the second derivative test, we see that f''(0) = 126, which is positive. This means that the local minimum at x = 0 is a relative minimum, and the graph of f(x) is concave up near x = 0.

At x = 7 and x = 9, we have simple zeros.

From the first derivative test, we see that f'(x) changes sign from positive to negative at x = 7 and from negative to positive at x = 9, indicating that f(x) has local maximums at x = 7 and x = 9.

From the second derivative test, we see that f''(7) = -42 and f''(9) = 54, so the local maximum at x = 7 is a relative maximum, and the local maximum at x = 9 is a relative minimum.

Thus,

The zeros of the function are x = 0, x = 7, and x = 9.

The graph of f(x) is concave down near x = 7 and concave up near x = 9.

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The zeros of the graph are 0, 7, and 9.

To find the zeros of the function, we can set it equal to zero and factor:

[tex]x^4 - 16x^3 + 63x^2 \\= x^2(x^2 - 16x + 63) \\= x^2(x - 7)(x - 9)[/tex]

So the zeros are x = 0, x = 7, and x = 9.

We may look at the function's sign on either side of each zero to understand how the graph behaves there. The function's factored form may be used to our advantage here:

Examining the leading coefficient (which is positive) and the degree of the polynomial will also reveal the graph's general behavior (which is even). This indicates that if x increases or decreases, the graph will be upward-facing and will go closer to infinity in both directions.

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The valid values for probability are: a) P(A) = 0.4, d) P(A) = 4/5, f) P(B) = 20% and h) P(A) = 0

From the question, we have the following parameters that can be used in our computation:

List of options

The valid values for probability are any value between 0 and 1 (inclusive)

This means that numbers less than 0 or greater than 1 are invalid

using the above as a guide, we have the following:

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Writing 1/(1 + x) + 2/(1 + x) as a single fraction , we get 3​/(1 + x)

From the question, we have the following parameters that can be used in our computation:

1/1_x+2/1+x​

Express properly

So, we have

1/(1 + x) + 2/(1 + x)

Take the LCM of the fractions

So, we have

(1 + 2)/(1 + x)

Evaluate the sum of like terms

3​/(1 + x)

HEnce, the solution si 3​/(1 + x)

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Answer:

16 tiles

Step-by-step explanation:

The slope of perpendicular line is -1.

We have,

Equation: 3x - 3y = 63

Now, writing the given equation in slope intercept form

3y= 3x- 63

y= 3x/ 3 - 63/3

y= x - 21

So, the slope of given equation is 1.

Now, the slope of two perpendicular line have the product -1.

let the slope of perpendicular line be m.

So, m x 1 = -1

m = -1

Thus, the slope of perpendicular line is -1.

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The car loan has a monthly payment of around $971.56. Based on the loan amount, annual percentage rate, down payment, and loan term, this is determined using the present value of an annuity formula.

Christina has put down the following amount:

10% down payment times $43,599 equals $4,359.90.

She must borrow the upcoming amount:

Loan amount = $43,599 - $4,359.90 = $39,239.10

We must apply the of an annuity formula to determine the monthly payment:

Present value of annuity

=  PV = A×((1 – (1 / (1 + r)⁻ⁿ)) / r)

If A is the monthly payment, then r denotes the annual interest rate, n the frequency at which interest is compounded annually, and t the number of years.

Due to the loan's three-year term and monthly compounding of interest, we have:

n = 12 and t = 3

The annual interest rate is 1.99%, but we need to convert it to a monthly interest rate by dividing it by 12:

r = 1.99% / 12 = 0.1667%

Substituting the given values, we get:

Present value of annuity = A × [1 - (1 + 0.01667)⁻¹²ˣ³] / (0.01667)

≈ $35,056.33

Therefore, the monthly payment is:

Monthly payment = $35,056.33 / (12 × 3) ≈ $971.56

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Two possible ways to write 9/10 as a sum of fractions are 1/2 + 4/5 and 3/5 + 3/10.

To write9/10 as a sum of  fragments, we need to find two  fragments with a common denominator that add up to9/10. One way to do this is to express9/10 as the sum of two  fragments with denominators that are multiples of 10.   One possible way to do this is   = 1/24/5   Both  fragments on the right- hand side have denominators that are multiples of 10, and when we add them together, we get9/10.

9 = 2x + y

We can then solve for x and y by trying different values until we find a solution that works. One possible solution is x=3 and y=3:

9/10 = 3/5 + 3/10

3/5 + 3/10 = 6/10 + 3/10 = 9/10

Since 9/10 is equal to 9/10, we have shown that 9/10 can be written as a sum of fractions.

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The probability of either the system or the backup working properly is 1 - 0.02 = 0.98. Which is 0.02 x 0.02 = 0.0004 or 0.04%. Therefore, the probability that neither the system nor its backup is working properly at the end of the 30 days is very low, only 0.04%.

To find the probability that neither the primary computer system nor the backup system is working properly at the end of the 30-day period, we'll need to use the given probability of each system working properly (98%) and the fact that the systems work or fail independently.

Step 1: Find the probability of each system failing
Since each system has a 98% chance of working properly, the probability of it failing is 100% - 98% = 2%.

Step 2: Calculate the probability that both systems fail
Since the systems work or fail independently, we can multiply the probabilities of each system failing together:
2% (primary failing) x 2% (backup failing) = 0.02 x 0.02 = 0.0004

Step 3: Convert the probability to a percentage
0.0004 x 100% = 0.04%

Therefore, the probability that neither the primary computer system nor its backup are working properly at the end of the 30-day period is 0.04%.

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To prove that any postage of at least 12 cents can be obtained using 3 cents and 7 cents stamps, we will use mathematical induction.

First, let's check the base case. We need to show that it's possible to obtain a postage of 12 cents using 3 cents and 7 cents stamps. We can do this by using two 3 cents stamps and two 7 cents stamps, for a total of 12 cents.
Now, let's assume that it's possible to obtain any postage of at least 12 cents using 3 cents and 7 cents stamps. We want to prove that this also holds for postage values of n+1.
To do this, we need to show that it's possible to obtain a postage of n+1 cents using 3 cents and 7 cents stamps, assuming that we can already obtain any postage of at least 12 cents.
Let's consider the case where n+1 is an odd number. We can use one 7 cents stamp and (n-6)/2 3 cents stamps to obtain a postage of n+1 cents. This works because if n+1 is odd, then n-6 must be even, so we can divide it by 2 and use that many 3 cents stamps.
Now, let's consider the case where n+1 is an even number. We can use two 3 cents stamps and (n-8)/2 7 cents stamps to obtain a postage of n+1 cents. This works because if n+1 is even, then n-8 must be even, so we can divide it by 2 and use that many 7 cents stamps.
Therefore, we have shown that it's possible to obtain any postage of at least 12 cents using 3 cents and 7 cents stamps, and our proof is complete.

To use mathematical induction to prove that any postage of at least 12 cents can be obtained using 3 cents and 7 cents stamps, follow these steps:
Step 1: Base case
Show that the statement holds true for the smallest value (12 cents).
You can obtain 12 cents using four 3-cent stamps (3+3+3+3). So, the base case is true.
Step 2: Inductive hypothesis
Assume the statement is true for some arbitrary value 'k' (k >= 12) such that k can be obtained using 3 cents and 7 cents stamps.
Step 3: Inductive step
Prove the statement is true for the next value, 'k+1'. We need to show that (k+1) cents can also be obtained using 3 cents and 7 cents stamps.
Case 1: If the 'k' postage contains at least one 3-cent stamp, we can replace that with a 3-cent and a 3-cent stamp to obtain (k+1) cents.
Case 2: If the 'k' postage contains only 7-cent stamps, we have at least two 7-cent stamps since k >= 12. We can replace two 7-cent stamps with five 3-cent stamps (7+7 = 3+3+3+3+3), which adds up to the same postage value. In this case, we can obtain (k+1) cents by adding another 3-cent stamp.
In both cases, (k+1) cents can be obtained using 3 cents and 7 cents stamps. Therefore, by mathematical induction, any postage of at least 12 cents can be obtained using 3 cents and 7 cents stamps.

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False. The statement you described is not an equivalent form for a conditional statement. The process you mentioned, which is reversing and negating the antecedent and consequent, is known as forming the contrapositive of the statement.

A conditional statement has the form "If P, then Q," where P is the antecedent and Q is the consequent. The contrapositive is formed by negating both the antecedent and consequent, and reversing their order: "If not Q, then not P." The contrapositive is equivalent to the original conditional statement.

However, simply reversing the antecedent and consequent without negating them gives you the converse, which is "If Q, then P." The converse is not equivalent to the original conditional statement.

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Answer: -1/3-(-3/5)=4/15

Step-by-step explanation:

P.S i'm emo

Answer:

22.98133...

Step-by-step explanation:

30 x cos(40°)

then refine to a decimal form

In summary, statement 1+2 is correct as it provides information about both c and a, while statement 1 alone and statement 2 alone are not sufficient to determine the value of a.

Statement 1+2: The first statement states that the value of c is not equal to zero, and for these values of c, a is always 1. The second statement states that h is equal to b*c, and since h is not equal to zero, neither b nor c can be zero. This means that statement 1+2 is correct, as it provides information about both c and a.

Statement 1: This statement provides information about the value of c, but it doesn't say anything about a. It states that h is equal to b*c and that h is not equal to zero, which means that neither b nor c can be zero. However, this information alone is not sufficient to determine the value of a.

Statement 2: This statement provides information about the relationship between a, c, and f. It states that c is equal to f, and a*c is equal to f. This expression can hold if c=f=0, but a can have any value. Additionally, if c and f are any non-zero value, a is always 1. This means that statement 2 alone is not sufficient to determine the value of a.

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Based on the definition of like terms, combining like terms in the expression, 8 + 7b - 10 + 2 would give us: 7b.

Like terms can be described as terms that have the same degree, or similar variables with the same power. For example, 2x and 3x have the same degree and the same variables, so they are like terms and can combined together.

Also, constants, that is, numbers without variables are also like terms that can be combined together. For example, given the expression, 6 - 5x + 3, the like terms are 6 and 3, and can be combined together.

Given the expression, 8 + 7b - 10 + 2, the like terms would be combined as follows:

7b + (8 - 10 + 2)

= 7b

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Increase in taxes is one of the reasons why the change in Mr. Henderson's net income

It is possible that Mr. Henderson's net income has decreased this month despite having received the same gross income as last month. Let us examine some of the plausible rationales behind it:

An increase in taxes: If Mr. Henderson worked more hours or obtained a raise, his gross income would be higher. However, if he now belongs to a higher tax bracket, he will owe more money in taxes and therefore have lower net income.

A change in deductions: It is likely that Mr. Henderson's employer may have modified his paycheck deductions which can lead to more taxes being held back from his earnings - an eventuality that could cause his net income to decrease.

Alterations in benefits: Changes in Mr. Henderson's approved employee benefits plan- insurance premiums increasing or retirement savings contributions stalling, for instance- could also explain why his net income reduced this month.

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The daily inpatient census for July 16 is 271.

To determine the daily inpatient census for July 16, we need to take into account the census at midnight on July 15, the number of discharges, admissions, and additional patients (content loaded) throughout the day on July 15 and July 16.

Starting with the census at midnight on July 15 of 239, we subtract the number of discharges (59) and add the number of admissions (67) and additional patients (24) to get the total number of patients in the hospital on July 16.

239 - 59 + 67 + 24 = 271

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Answer: -2

Step-by-step explanation:

f(4) is asking us that when x=4, what is the value of y?

Looking at the graph, you can tell that the point is: (4, -2)

Therefore, the answer is -2.

The value of x in the quadrilateral is 20 degrees.

The sum of angles in a quadrilateral is 360 degrees. Therefore, a quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angle.

Hence, let's find the value of x in the quadrilateral.

x + x + 32 + 8x - 16 + 8x - 16  = 360

2x + 16x + 32 - 32 = 360

18x + 0 = 360

18x = 360

18x = 360

divide both sides by 18

x = 360 / 18

x = 20

Therefore,

x = 20 degrees

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Answer:     3 million

Step-by-step explanation:

180 divided by 60 equals 3 so that would be 3 million because there are only 60 thousand and that would be a million because it would not be a billion.

The probability that Tate will hit 2 home runs in a row is P ( R ) = 4/81

Given data ,

Let the total number of throws be = 9

And , the number of times Tate hits a home run in 9 throws = 2

Now , the probability of Tate hitting a home run in a single at-bat is 2/9

The probability of hitting a home run in two consecutive at-bats is the product of the probabilities of hitting a home run in each individual at-bat, assuming that the outcomes of the at-bats are independent.

Therefore, the probability of Tate hitting 2 home runs in a row is P ( R )

P ( R ) = (2/9) x (2/9)

P ( R ) = 4/81

Hence , the probability is 4/81

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The equation of the circle is x² + y² = 4 and the equation of the line is       y = 0.5x + 1

A circle is a closed curve that is drawn from the fixed point called the center, in which all the points on the curve are having the same distance from the center point of the center. The equation of a circle with (h, k) center and r radius is given by:

(x-h)^2 + (y-k)^2 = r^2

This is the standard form of the equation. Thus, if we know the coordinates of the center of the circle and its radius as well, we can easily find its equation.

In this problem, we need to just take two points as the diameter and then write out the equation of the circle.

Taking the points (-2, 0) and (2, 0)

The equation of the circle is ;

x² + y² = 4

This shows that h and k are 0.

The equation of the line can also be calculated as;

y = mx + c

m = slope of the line

m = y₂ - y₁ / x₂ - x₁

m = 2 - 0 / 2 - (-2)

m = 2 / 4

m = 1/2

The y-intercept is the point at which the line touches the y-axis

y = 1

The equation of the line is y = 1/2x + 1

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Alma has to utilize 6/5 glasses of blue paint and 6/5 mugs of ruddy paint with the 2 mugs of white paint to create 2 glasses of her favorite shade of purple paint.

To form 5 mugs of purple paint, Alma makes use of 3 mugs of blue paint, 1frac{1}{2} glasses of ruddy paint, and frac{1}{2} a container of white paint.

So, to form 1 container of purple paint, she has to utilize:

3/5 glasses of blue paint

1frac{1}{2}/5 cups of ruddy paint

frac{1}{2}/5 mugs of white paint

Presently, Alma needs to form 2 glasses of purple paint utilizing 2 glasses of white paint.

Since she already has frac{1}{2} a container of white paint, she as it were needs another 1frac{1}{2} mugs of white paint.

To form 2 glasses of purple paint, Alma must twofold the sum of each color utilized to create 1 glass of purple paint.

In this way, she will require:

2 * 3/5 = 6/5 glasses of blue paint

2 * 1frac{1}{2}/5 = 3/5 + 3/5 = 6/5 glasses of ruddy paint

2 * frac{1}{2}/5 = 1/5 cups of white paint

Since she as of now has 2 glasses of white paint, she will as it were ought to utilize 1/5 glasses of the white paint that she as of now has.

Subsequently, Alma has to utilize 6/5 glasses of blue paint and 6/5 mugs of ruddy paint with the 2 mugs of white paint to create 2 glasses of her favorite shade of purple paint.

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The measure of the missing angle is38 degrees.

The figure in the image is a right triangle.

Missing angle θ = ?

Hypotenuse = 55

Opposite to angle θ = 34

To find the missing angle, we use the trigonometric ratio.

sine = opposite / hypotenuse

Plug in the given values and solve for the missing angle.

sinθ = 34/55

Take the sine inverse

θ = sin⁻¹( 34/55 )

θ = 38⁰

Therefore, the angle is 38 degrees.

Option A) 38⁰ is the correct answer.

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Your average waiting time will be approximately 1 minute.

As the first passenger, you will not have to wait for any other passengers to get in the taxi. However, the taxi will wait for 2 passengers to arrive or 3 minutes to pass since your boarding.

Since passengers arrive according to a Poisson process with an average of 60 passengers per hour, the arrival rate lambda can be calculated as:

lambda = average number of passengers per time unit = 60/60 = 1 passenger per minute

The time between two consecutive passenger arrivals follows an exponential distribution with parameter lambda. Thus, the probability of waiting less than t minutes for the second passenger to arrive can be calculated as:

P(wait < t) = 1 - e^(-lambda*t)

We need to find the average waiting time until the second passenger arrives. This can be calculated as the area under the probability distribution curve divided by the arrival rate lambda:

average waiting time = integral from 0 to infinity of t*(1 - e^(-lambda*t)) dt / lambda

Using integration by parts, we can solve this integral to get:

average waiting time = 1/lambda + (1 - e^(-lambda*t))/(lambda^2)

Plugging in the values, we get:

average waiting time = 1/1 + (1 - e^(-1*3))/(1^2) = 1 + (1 - 0.0498) = 1.9502 minutes

Therefore, as the first passenger, your average waiting time until the second passenger arrives is 1.9502 minutes.

To answer your question, let's consider the two possible scenarios:

1. Two passengers are collected: In this case, the first passenger (you) waits for the second passenger to arrive. Since the arrival rate is 60 passengers per hour, the average time between arrivals is 1 minute (60 minutes / 60 passengers).

2. Three minutes have expired: In this case, the taxi departs after 3 minutes even if only one passenger (you) is in the taxi.

On average, the waiting time for the first passenger (you) will be the minimum of these two scenarios. Thus, your average waiting time will be approximately 1 minute.

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The pooled standard deviatio is 5.746. We can say with 95% confidence that the true difference between the population means falls between -4.019 and 0.719.

First, we need to calculate the pooled standard deviation:

s_p = sqrt(((n1-1)*s1^2 + (n2-1)*s2^2)/(n1+n2-2))

s_p = sqrt(((6-1)*5.9^2 + (7-1)*5.6^2)/(6+7-2))

s_p = 5.746

Next, we can calculate the t-statistic:

t = ((x1 - x2) - 0) / (s_p * sqrt(1/n1 + 1/n2))

t = ((72.9 - 75.1) - 0) / (5.746 * sqrt(1/6 + 1/7))

t = -0.956

Using a t-distribution table with conservative degrees of freedom (df = min(n1-1, n2-1) = 5), we find that the critical value for a one-tailed test with α=0.05 is -1.833. Since our calculated t-statistic is greater than the critical value, we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is sufficient evidence to support the claim that the first population mean is less than the second population mean.

As for the confidence interval, we can use the formula:

(x1 - x2) ± t_(α/2, df) * s_p * sqrt(1/n1 + 1/n2)

Plugging in the values:

(72.9 - 75.1) ± t_(0.025, 5) * 5.746 * sqrt(1/6 + 1/7)

-4.019 < μ1 - μ2 < 0.719

Therefore, we can say with 95% confidence that the true difference between the population means falls between -4.019 and 0.719.

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