Determine whether each of these integers is prime a) 2 1 b) 2 9 c) 7 1 d) 9 7 e) 1 1 1 f) 1 4 3 Calculate a) GcD (12, 18) b) GcD (33,44 ) c) GcD (21,55) d) LcM (10, 15)

Probability is the possibility that something will happen or is the degree of likelihood of an event. It's a number that reflects the likelihood of an occurrence.

Probability is expressed as a number ranging from 0 to 1, with 0 indicating that an event is impossible and 1 indicating that it is certain to happen. A probability of 0.5, for example, represents a 50% chance that the event will occur. Types of Probability1. Empirical Probability: Empirical probability is a measure of how frequently an event occurs based on past experiences or experiments.

Theoretical probability is the probability of an event occurring based on mathematical calculations or formulas.3. Subjective Probability: Subjective probability is a probability based on personal judgment, experience, and intuition. It is not based on data or calculations but on what the person believes or feels to be true. The probability mentioned in the problem is a subjective probability.

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Answer:

1

4

(2.718282)−2f−

1

f

−(2)(2.718282)

=

−2f2−4.756993f−1

f

=

−8f2−19.027973f−4

4f

=

−8f2−19.027973f−4

4f

Answer:

She started with 50 stamps

Step-by-step explanation:

Hi! For these types of problems we always result to going backwards. So, she now has 30 right? So, to reverse into the problem, we do the opposite of what it says. "She then bought five more" 30 - 5 = 25. Then it says she sold half of them. 25 x 2 = 50. If we recheck by going back, she sold half of them (50 / 2 = 25) and she bought five more (25 + 5 = 30).

Hope this helps!

Answer: B.) y = 4/3x + 1

The square root of a number can also be negative number so x could also be -9

Square root of a number is the number such that if it is multiplied by itself we get the square. The opposite of squaring an integer is finding its square root. As we know multiplication of two negative numbers produce a positive number. this is the reason why square of both positive and negative numbers are both positive. therefore, square root of a number can also be positive or neegative both. That is why we can't take square root of negative numbers.

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Answer:

-2 is the answer

Step-by-step explanation:

Answer:

I have know idea what the answer is

The housing supply function is given by h(I,R) = a log1 + bR + cR log1. The housing supply responds to changes in I with a rate of a, and to changes in R with a rate of b + c log1.

Based on the given equation, the housing supply (h) is determined by two variables: I and R. The equation shows that h is a function of R, with a log-linear relationship. The variable I only appears as a constant (a) in the equation, so changes in I do not directly affect the supply of houses.
On the other hand, changes in R (or OR, which is the same variable) do affect the supply of houses. Specifically, an increase in R leads to an increase in the supply of houses. The magnitude of this increase depends on the values of b and c in the equation.
To see this, we can take the partial derivative of h with respect to R:
dh/dR = b + cR/(ln(10))
This equation tells us how much the housing supply changes in response to a change in R. The derivative is positive (i.e. the supply increases) as long as c is positive. The larger c is, the greater the increase in supply for a given increase in R.
Therefore, the correct answer is:
b + cR/(ln(10))

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Answer:

73.5 feet

Step-by-step explanation:

The length of a tree =42 feet

Mr. Ash estimates that this tree is 75% as tall now as it will be when fully grown.

We need to find the length of the tree when it is fully grown. It means we need to find the 75% of 42 and adding 42 to it as follows :

\(T=75\%\times 42+42\\\\=\dfrac{75}{100}\times 42+42\\\\=73.5\ ft\)

So, the tree will be 73.5 feet tall when it is fully grown.

10. 87 is higher than 44 automatically making us round up

True. The variance and standard deviation both quantify how far spaced apart a set of data is from the mean. They cannot be used to calculate the dispersion around the median or mode, or any other center-of-mass metric.

The variance and standard deviation both quantify how far spaced apart a set of data is from the mean. They can therefore be used to calculate the difference between the highest and lowest values in a data set. The standard deviation, which is the square root of the variance, is used to calculate how far away from the mean each result is on average. The average of the squared deviations between each data point and the mean is the variance. The variance and standard deviation cannot be used to quantify the dispersion of data around other measures of center, such as the median or mode, because they only measure the dispersion of data around the mean.

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Answer:

the second dimension 2D

Answer:

a) 60,000 cubic cm

b)600,000 cubic mm

c)60 L

Step-by-step explanation

To find the volume, you would have to multiply the height length and width.

50*40*30 and that equals to 60,000 cm. 10 mm=1cm.

So 60,000*10=b, b=600,000,  1,000 cm=1 L

60,000/1,000=L, L=60

Hope this helps. If it does, please rate 5 stars!

Answer:

Bottom right

Step-by-step explanation

Answer:

first answer is correct

Answer:

144

Step-by-step explanation:

4*3=12

12*12=144

The Taylor series for a function f about x=1 is an infinite sum that represents the function using its derivatives at x=1. It starts with the value of the function at x=1 and includes terms involving higher derivatives multiplied by powers of (x-1) divided by factorials. It allows us to approximate the function near x=1 using a polynomial.

1. The first term, f(1), represents the value of the function at x=1.
2. The subsequent terms involve the derivatives of the function at x=1. The second term, f'(1)(x-1), is the first derivative of f at x=1 multiplied by (x-1).
3. Each subsequent term involves higher derivatives of f at x=1, with each derivative being multiplied by (x-1) raised to a power and divided by the corresponding factorial.

The Taylor series is a way to represent a function as an infinite sum of terms derived from its derivatives at a specific point. In this case, the Taylor series for function f about x=1 is given by f(x) = f(1) + f'(1)(x-1) + f''(1)(x-1)^2/2! + f'''(1)(x-1)^3/3! + ...

Each term involves a derivative of f evaluated at x=1, multiplied by (x-1) raised to a power and divided by the corresponding factorial. By including more terms in the series, we can approximate the function better near x=1 using a polynomial.

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1. height(in.)

2. arm span (in.)

3. (30,27)

melody had 120 stamps.

and she gave Jeremy 30 stamps .

so she had 90 stamps now.

after she gave Jeremy 30 stamps,she had twice as much as him.

so 90 is 45+45 .other way 45 is half of 90.

so Jeremy had 45 stamps now.

they have altogether 90+45=135 stamps.

the answer is 135

By creating and solving an algebraic equation, we learn that Jeremy started with 60 stamps and Melody started with 180 stamps. Therefore, they originally had 240 stamps combined.

We'll use algebra to solve this. Let's let Jeremy's number of stamps be represented by J. According to the information, Melody had 120 more stamps than Jeremy before she gave him 30, so she had J + 120 stamps. After transferring the 30 stamps, she has J + 120 - 30 stamps, which simplifies to J + 90 stamps. According to the problem, this amount is twice the amount Jeremy has after receiving the 30 stamps (J + 30). So, we can set up this equation: 2(J + 30) = J + 90.

Solving this equation gives J = 60. That means Jeremy started with 60 stamps. Therefore, Melody started with 60 + 120 = 180 stamps. The total number of stamps both had originally is 60 + 180 = 240 stamps.

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The answer is 59/60.

and in decimal form it would be, 0.983333

Answer:

75 degrees

Step-by-step explanation:

on the long line that goes out to 132 is a supplementary line so that means the angle next to 132 will make the line equal 180

180 - 132 = 48

so now we know the inside angles are 48 and 57

A triangle has 180 degrees in it so

x + 48 + 57 = 180

x + 105 = 180

x = 75

The dimensions of the garden that minimize the cost are approximately 8.67 feet by 21.68 feet.

Let's assume the length of the rectangular garden is L and the width is W. Then the area of the garden is:

A = L * W = 188

We want to minimize the cost of enclosing the garden, which is given by:

C = 20L + 10(2L + W) = 20L + 20L + 10W = 40L + 10W

We can use the equation for the area of the garden to express one of the dimensions in terms of the other. For example, we can solve for W:

W = A / L = 188 / L

Substituting this expression for W into the cost equation, we get:

C = 40L + 10(A / L)

Taking the derivative of this expression with respect to L and setting it equal to zero to find the critical point(s):

dC/dL = 40 - 10(A / L^2) = 0

Solving for L, we get:

L^2 = A * 4/10 = 75.2

L ≈ 8.67 feet

Substituting this value of L back into the expression for W, we get:

W ≈ 21.68 feet

Therefore, the dimensions of the garden that minimize the cost are approximately 8.67 feet by 21.68 feet.

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The height that describes how tall the tree is is 37.5 feet.

To determine how tall the tree is, we need to apply the proportion formula to arrive at the right answer. We express the values this way:

\(\frac{x}{75} = \frac{50}{30}\)

Now we cross multiply to have

30x = 1125

x = 1125/30

= 37.5

So, the length of the tree is 37.5 feet.

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Answer:

Option B. ( x + 2, y - 1 ) is the correct answer.

Step-by-step explanation:

First of all, we have to write the coordinates of vertices of both triangles and then compare the respective vertices to find the rule,

So the vertices are:

A(-4,2) , B(-3,4) and C(-1,1)

A'(-2,1), B'(-1,3) and C'(1,0)

By comparing respective vertices we can observe that

A(-4,2) => (x+2,y-1) => A'(-2,1)

B(-3,4) => (x+2,y-1) => B'(-1,3)

C(-1,1) => (x+2,y-1) => C'(1,0)

Hence,

Option B. ( x + 2, y - 1 ) is the correct answer.

To determine the value of n in the binomial expansion of (4x + 2y)ⁿ, given that the expansion includes an x⁷y⁸ term, we need to find the exponent of the x term. In this case, the exponent of x is 7, so n would be 15.

The binomial expansion of (4x + 2y)ⁿ can be expressed using the binomial theorem, which states that each term in the expansion can be calculated using the formula:

\(C(n, k) * (4x)^{(n-k)} * (2y)^k\)

Here, C(n, k) represents the binomial coefficient, indicating the number of ways to choose k elements from a set of n elements. The term x⁷y⁸ implies that the x term is raised to the power of 7 and the y term is raised to the power of 8.

Since the exponent of the x term is (n-k), and in this case, it is 7, we can set up the equation (n-k) = 7. We also know that the exponent of the y term is equal to 8. Therefore, we can write the equation as:

(n - 7) = 7

By solving this equation, we find that n = 15. Thus, when the binomial expansion of (4x + 2y)ⁿ includes an x⁷y⁸ term, the value of n is 15.

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We're asked to develop a polynomial

Integer coefficient that has zero at 3 is (x-3)

Multiplicity of 2 gives (x - 3) (x - 3)

And a zero at -5/4 gives (x + 5/4)

Put together, we have: (x - 3) (x - 3)(x + 5/4) = (x - 3)^2 (x + 5/4) = 0

Answer:

7:24pm

Step-by-step explanation:

At 50 mph, it will take 195/50 = 3.9 hours to reach London

3.9 hours = 3 .9 * 60 = 3 hours and 54 minutes(54 = 0.9 * 60 )

3:30 + 3:34 ==> 7:24

(one way to do this is to add up the hours and minutes separately so we get 6:84) Since 84 minutes = 1 hour and 24 minutes, just add 1:24 to 6 to get 7:24

Another way to do this is to see that if the distance was 200 miles, then it would take exactly 4 hours (200/50) to reach at 7:30pm But it is short by 5 miles. At the speed of 50mph, the time taken to travel 5 miles = 60/50 * 5 = 6 minutes so deduct 6 minutes from 7:30pm to get 7:24pm

If the train is slower average speed, then the arrival time is delayed beyond 7:24pm

Answer:

He paid $9 twelve times

12× 2= 24 days

Step-by-step explanation:

1st day = $16.60

3rd day=$ 9 (i.e for every 2days afterwards)

5th day=$ 9

Yuri pays : 124.60

124.60-16.60

= $108.00

After paying the first day he paid 108.00

108.00÷ 9 = 12

He paid $9 twelve times

12× 2= 24 days

Therefore, the degree measures of the angles in the triangle KLM are: m∠K = 62°, m∠L = m∠M = 59°.

In an isosceles triangle, the base angles (the angles opposite the equal sides) are congruent. Let's denote the degree measure of each base angle as y.

Given that m∠K = (5x + 22)° and m∠LM = (4x + 27)°, we can set up an equation based on the fact that the sum of the angles in a triangle is 180°.

Since KLM is an isosceles triangle, we have:

m∠K + m∠L + m∠M = 180°

Substituting the given values, we have:

(5x + 22) + y + (4x + 27) = 180

Combine like terms:

9x + 49 + y = 180

Now, since KLM is isosceles, we know that m∠L = m∠M, so we can substitute y for (4x + 27)°:

9x + 49 + 4x + 27 = 180

Combine like terms:

13x + 76 = 180

Subtract 76 from both sides:

13x = 180 - 76

13x = 104

Divide by 13:

x = 104/13

x = 8

Now, we can substitute the value of x back into the equations to find the degree measure of each angle:

m∠K = (5x + 22)° = (5 * 8 + 22)° = 62°

m∠L = m∠M = (4x + 27)° = (4 * 8 + 27)° = 59°

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Answer:

82-5(15)=18-75=7

Step-by-step explanation:

Answer:

the square of hypotenuse rs eqaul to the sum of the square of the legs