Under the following translation, (x,y) becomes (x-2, y+2) the point (1,1) will become _____.

There are 11 prime dates in it.

The prime numbers between 1 and 30 are 1, 2,3,5,7,11,13,17,19,23,29

Relative prime:

Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and 14 are not.

Hence There are 11 prime dates in the month of June.

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Answer: 10

Step-by-step explanation:

Since exactly 1 in every $n$ consecutive dates is divisible by $n$, the month with the fewest relatively prime days is the month with the greatest number of distinct small prime divisors. This reasoning gives us June ($6=2\cdot3$) and December ($12=2^2\cdot3$). December, however, has one more relatively prime day, namely December 31, than does June, which has only 30 days. Therefore, June has the fewest relatively prime days. To count how many relatively prime days June has, we must count the number of days that are divisible neither by 2 nor by 3. Out of its 30 days, $\frac{30}{2}=15$ are divisible by 2 and $\frac{30}{3}=10$ are divisible by 3. We are double counting the number of days that are divisible by 6, $\frac{30}{6}=5$ days. Thus, June has $30-(15+10-5)=30-20=\boxed{10}$ relatively prime days.

The probability that the UGA Einstein will score at least a 415 on the SAT math is approximately 0.1587, or 15.87%.

To find the probability that the UGA student will score at least a 415 on the SAT math, we need to calculate the area under the normal distribution curve.

First, we need to standardize the score using the z-score formula:

z = (x - μ) / σ

where x is the desired score, μ is the mean, and σ is the standard deviation.

In this case, x = 415, μ = 400, and σ (standard deviation) is the square root of the variance, which is √225 = 15.

Calculating the z-score:

z = (415 - 400) / 15

z ≈ 1

Next, we can use a standard normal distribution table or a calculator to find the probability associated with a z-score of 1. The table or calculator will provide the area under the curve to the left of the z-score.

The probability that the UGA student will score at least a 415 is equivalent to finding the area to the right of the z-score (or 1 minus the area to the left).

P(Z ≥ 1) ≈ 1 - P(Z < 1)

Looking up the corresponding value in the standard normal distribution table or using a calculator, we find that P(Z < 1) is approximately 0.8413.

Therefore, P(Z ≥ 1) ≈ 1 - 0.8413 = 0.1587.

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Answer:

Sqrt 26 = 5.1

Step-by-step explanation:

Sqrt [(1-6)^2 + (3-2)^2]

= sqrt (25+1) = sqrt 26 = 5.1

Answer:

Yes it is 7 cuz it has the equation of 3-5a

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Plug in -3 as a

h(-3) = (3+15)/3

h(-3) = 18/3

h(-3) = 6

Answer:

The length of side PQ is 2 units.

The length of side QR is 2.24 units.

The perimeter of the parallelogram PQRS is about 8.48 units.

Step-by-step explanation:

The given figure is as follows :

To find - The length of side PQ is ....... units.

              The length of side QR is about ......... units.

               The perimeter of the parallelogram PQRS is ........

Solution -

From the figure , we can see that

P = (-5, 3)

Q = (-3, 3)

R = (-4, 1)

S = (-6, 1)

Now,

By distance formula, we get

PQ = √(3 - 3)² + (-3 + 5)²

     = √0 + 2²

     = √4

     = 2

∴ we get

The length of side PQ is 2 units.

Now,

QR = √(1 - 3)² + (-4 + 3)²

     = √(-2)² + (-1)²

     = √4 + 1

     = √5

     = 2.236

∴ we get

The length of side QR is 2.24 units.

Now,

We know that,

Perimeter of Parallelogram = 2(a + b) where a is the base and b is the side

Here Given that,

a = 2

b = 2.24

So,

Perimeter of parallelogram PQRS = 2(2 + 2.24)

                                                         = 2(4.24)

                                                         = 8.48

∴ we get

The perimeter of the parallelogram PQRS is about 8.48 units.

Answer:

PQ 2 units

QR 2.24 units.

Step-by-step explanation:

i did the test

There are 56 such combinations possible.

To find the number of ways to assign three jobs to eight employees if each employee can be given more than one job, we can use the combination formula.
The formula for combination is:
nCr = n! / (r!(n-r)!)
where n is the total number of items, r is the number of items being selected, and ! denotes factorial (the product of all positive integers up to that number).
In this case, we have 8 employees and we need to select three jobs. Therefore, we can use the combination formula as follows:
8C3 = 8! / (3!(8-3)!)
= 8! / (3!5!)
= (8x7x6) / (3x2x1)
= 56
Therefore, there are 56 ways to assign three jobs to eight employees if each employee can be given more than one job.
To illustrate this further, let's assume that the three jobs are A, B, and C. One possible way of assigning these jobs to employees could be:
Employee 1: A, B
Employee 2: B, C
Employee 3: A, C
Employee 4: A, B
Employee 5: B, C
Employee 6: A
Employee 7: B
Employee 8: C
As we can see, each employee has been given at least one job and some employees have been given more than one job. There are 56 such combinations possible.

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Answer:

The picture isn't showing up for me

To determine the probability that the ball selected shows an odd number, given that the ball is yellow, we need to consider the number of favorable outcomes (yellow balls showing odd numbers) and the total number of possible outcomes (yellow balls).

From the given information, we can identify two favorable outcomes: the yellow balls numbered 3 and 5.

Therefore, the probability that the ball selected shows an odd number, given that the ball is yellow, is:

Probability = (Number of favorable outcomes) / (Number of total outcomes)

= 2 / 3

= 2/3 ≈ 0.6667

Probability that the ball selected shows an odd number, given that the ball is yellow, is approximately 0.6667 or 66.67%.

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Answer:

2 + y > 16

Step-by-step explanation:

the sum of 2 and y is greater than 16

                   2 + y           >                   16

2 + y > 16

Answer:

664

Step-by-step explanation:

651 - - 13

Negative times negative is positive.

651 + 13

Add.

664

Answer:

664

Step-by-step explanation:

651 - (-13)

Do the keep , change , change method

So , it will be :

651 + 13 = 664

Hope this helps and plsss plss amrl as brianliest and THNXX :)

Answer:

Melanie has 28 cousins.

Step-by-step explanation:

4 x 7 = 28

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

An equation that represents a line that is perpendicular to line b which passes through the points (2, -6) and (-8, 9), and that passes through the point (-12, -3) is 3y = 2x + 15.

Line b passes through the points (2, -6) and (-8,9). Therefore the slope of line b is

slope = Δy/ Δx

= (9 - (-6))/ (-8 - 2)

= -1.5

Slope of two perpendicular lines follows the property that product of their slopes equals -1. Therefore slope of a line perpendicular to line b, m is

m × (-1.5) = -1

m = 2/3

Therefore we have slope of the line and and a point through which the line passes, (-12, -3). The general equation of a straight line is y = mx + c. Substituting m = 2/3 and the point (-12, -3) we can find the value of c.

-3 = 2/3 × (-12) + c

c = 8 - 3 = 5

Therefore the equation of line is y = 2/3x + 5, that is 3y = 2x + 15.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

Diagram

x = ?

y = ?

z = ?

Step 02:

Similar Triangles

15 * 20 = z * z

300 = z ²

x ² + 15 ² = z ²

y² + z² = 20²

The answer is:

x = √75 = 5√3

y = 10

z = √300 = 10√3

The monthly payments for a $22,000 car loan with a 4-year term, 7% APR, and no down payment required would be $398.48.

To calculate the monthly payments on a 4-year loan with an annual percentage rate (APR) of 7 percent and no down payment required, we can use the formula for calculating the monthly payment on an amortizing loan. The formula is:M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:M = Monthly payment

P = Principal amount (loan amount)

r = Monthly interest rate (APR divided by 12 months)

n = Total number of payments (number of years multiplied by 12 months)

In this case, the principal amount (P) is $22,000, the annual interest rate (APR) is 7 percent, and the loan term is 4 years.First, we need to convert the annual interest rate to a monthly rate by dividing it by 12:

r = 0.07 / 12 = 0.00583

Next, we calculate the total number of payments:

n = 4 * 12 = 48

Now, we can plug in the values into the formula:

M = 22,000 * (0.00583 * (1 + 0.00583)^48) / ((1 + 0.00583)^48 - 1)

Calculating this expression will give us the monthly payment.

The correct answer is $398.48.

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Step-by-step explanation:

\(3)b \: c \ \: d \: e \\ \\ 4)bc \: nd \: de \\ 5)s \\ 6)t \\ thank \: you\)

The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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To report the $39.1 million debt on its December 31, 2024, balance sheet, Bahamas Airlines would classify the debt into two categories: current liabilities = $6,200,000 and long-term liabilities =  $32,900,000.

To report the $39.1 million debt on its December 31, 2024, balance sheet, Bahamas Airlines would classify the debt into two categories: current liabilities and long-term liabilities.

Current Liabilities: The portion of the debt that is due within the next year, which is $6.2 million, would be reported as a current liability. This amount represents the short-term portion of the debt that needs to be repaid within the next year.

Long-Term Liabilities: The remaining portion of the debt, which is the difference between the total debt and the current liability, would be reported as a long-term liability. In this case, it would be $39.1 million - $6.2 million = $32.9 million.

Therefore, Bahamas Airlines would report the $39.1 million debt on its December 31, 2024, balance sheet as follows:

Current Liabilities:

Debt due within the next year: $6,200,000

Long-Term Liabilities:

Debt due after one year: $32,900,000

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use this formula and solve the question

AREA OF BASE = 1 by 2 ×base × Height

To find ℒ{f(t)}, we can apply the definition of the Laplace transform:

ℒ{f(t)} = ∫[0,∞) e^(-st) f(t) dt

For the given function f(t), we have:

f(t) = {cos(t), 0 ≤ t ≤ π

0, t ≥ π

Therefore, we can split the integral into two parts based on the intervals of f(t):

ℒ{f(t)} = ∫[0,π) e^(-st) cos(t) dt + ∫[π,∞) e^(-st) * 0 dt

Simplifying the second integral:

∫[π,∞) e^(-st) * 0 dt = 0

Now let's focus on the first integral:

ℒ{f(t)} = ∫[0,π) e^(-st) cos(t) dt

To solve this integral, we can use the property of the Laplace transform:

ℒ{cos(t)} = s / (s^2 + 1)

Applying this property to the integral:

ℒ{f(t)} = ∫[0,π) e^(-st) cos(t) dt = ∫[0,π) e^(-st) * ℒ{cos(t)} dt

= ∫[0,π) e^(-st) * (s / (s^2 + 1)) dt

Now we can integrate the expression:

ℒ{f(t)} = ∫[0,π) (s / (s^2 + 1)) e^(-st) dt

This integral can be solved using standard techniques of integration. The result will be a function of s.

Unfortunately, it is beyond the scope of a simple text-based conversation to provide the exact solution to this integral. However, the Laplace transform of f(t) will be a function of s, involving exponential and trigonometric terms.

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Step-by-step explanation:

tan(2pi) = 0

tan(a + b) = (tan(a) + tan(b))/ (1 - tan(a) * tan(b))

tan(theta + 2pi)

= tan(theta) + tan(2pi) / 1 - (tan(theta) * tan(2pi))

= tan(theta) + 0 / 1 - tan(theta) * 0

= tan(theta) / 1

= tan(theta)

Answer:

2x-1

Step-by-step explanation:

Answer:

= 2x + (-1)

Step-by-step explanation:

Let's simplify step-by-step.

2x+4−5

=2x+4+−5

Combine Like Terms:

=2x+4+−5

=(2x)+(4+−5)

=2x+−1

Answer: C, D, and E are the answers

Answer:

Anwer is C, D, E

Step-by-step explanation:

Slopes of Parallel and Perpendicular Instructions:

Question 1: -3, 1/3

Question 2: y = 4x + 4

Question 3: 1/4, -4, 1/4, -4

Question 4: C, D, E

You will have R1157.63 in the bank after 3 years if you invest R1000 at 5% per year.

We can use the formula for compound interest to calculate the total amount you will have in the bank after 3 years if you invest R1000 at 5% per year. The formula is:

\(A = P(1 + r/n)^(n*t)\)

where:

A is the total amount

P is the principal (initial amount)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time in years

In this case, P = R1000, r = 0.05, n = 1 (since the interest is compounded annually), and t = 3. Substituting these values into the formula, we get:

\(A = 1000(1 + 0.05/1)^(1*3)\)

\(= 1000(1.05)^3\)

= 1000(1.157625)

= R1157.63 (rounded to two decimal places)

Therefore, you will have R1157.63 in the bank after 3 years if you invest R1000 at 5% per year.

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Find the total amount I will have in the bank after 3 years if I invest R1000 at 5% per year?

1. T3 is found using the formula \(T3 = (T2 - T1) / r + T2\), which gives T3 = 100 °C.

2. To calculate the heat required to convert ice to steam:

  a) Heating the ice requires Q1 = 250.8 J.

  b) Melting the ice requires Q2 = 4008 J.

  c) Heating the water requires Q3 = 5025.6 J.

  d) Vaporizing the water requires Q4 = 27120 J.

  The total heat required is 36604.4 J.

Therefore, T3 is 100 °C, and it takes 36604.4 J of heat to convert 12.0 g of ice at -10.0 °C to steam at 100.0 °C.

To solve the given problem, we need to apply the concepts of specific heat capacity and latent heat.

1. Determining T3:

We are given two temperatures: T1 = -30 °C and T2 = 70 °C, and a rate of change, r = 5. We can use the formula

\(\[ T3 = \frac{{(T2 - T1)}}{r} + T2 \]\), to find T3.

Substituting the values into the formula:

\(\[ T3 = \frac{{(70 - (-30))}}{5} + 70 \]\)

Therefore, T3 is equal to 100 °C.

2. Calculating the heat required to convert ice to steam:

To find the heat required, we need to consider the phase changes and the temperature changes.

a) Heating the ice from -10.0 °C to 0 °C:

We need to use the concept of specific heat capacity \((\(c\))\) to calculate the heat required. For ice, the specific heat capacity is 2.09 J/g°C. The mass of ice is given as 12.0 g. The temperature change is \(\(\Delta T = 0 - (-10.0) = 10.0\)\) °C.

The heat required to heat the ice is given by:

\(\[ Q1 = m \cdot c \cdot \Delta T \]\)

Substituting the values:

\(\[ Q1 = 12.0 \, \text{g} \cdot 2.09 \,\)J/g°C. 10.0°C

b) Melting the ice at 0 °C:

We need to consider the latent heat of fusion \((\(L_f\))\) to calculate the heat required. For ice, the latent heat of fusion is 334 J/g. The mass of ice is still 12.0 g.

The heat required to melt the ice is given by:

\(\[ Q2 = m \cdot L_f \]\)

Substituting the values:

\(\[ Q2 = 12.0 \, \text{g} \cdot 334 \, \text{J/g} \]\)

c) Heating the water from 0 °C to 100 °C:

We use the specific heat capacity of water, which is 4.18 J/g°C. The mass of water is also 12.0 g. The temperature change is \(\(\Delta T = 100 - 0 = 100 °C\)\).

The heat required to heat the water is given by:

\(\[ Q3 = m \cdot c \cdot \Delta T \]\)

Substituting the values:

\(\[ Q3 = 12.0 \, \text{g} \cdot 4.18 \,\) J/g°C.100°C

d) Vaporizing the water at 100 °C:

We need to consider the latent heat of vaporization \((\(L_v\))\) to calculate the heat required. For water, the latent heat of vaporization is 2260 J/g. The mass of water is still 12.0 g.

The heat required to vaporize the water is given by:

\(\[ Q4 = m \cdot L_v \]\)

Substituting the values:

\(\[ Q4 = 12.0 \, \text{g} \cdot 2260 \, \text{J/g} \]\)

Finally, the total heat required is the sum of the individual heat:

\(\[ \text{Total heat} = Q1 + Q2 + Q3 + Q4 \]\)

Substituting the calculated values for Q1, Q2, Q3, and Q4:

\(\[ \text{Total heat} = 250.8 \, \text{J} + 4008 \, \text{J} + 5025.6 \, \text{J} + 27120 \, \text{J} \]\)

Therefore, it takes 36604.4 J of heat to convert 12.0 g of ice at -10.0 °C to steam at 100.0 °C.

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Answer:

y = -1+ 1/4x

Step-by-step explanation:

x - 4y = 4

subtract x from both sides to isolate y

-4y = 4 - x

divide both sides by -4

y = -1 + 1/4x

Answer:

perpendicular lines.

Step-by-step explanation:

Two lines are said to be perpendicular if they meet or cross or intersect ..

Answer:

\(\huge\boxed{-1}\)

Step-by-step explanation:

\(\frac{-5^2}{(-5)^2}\)

=> \(\frac{-25}{25}\)

=> -1

Answer:

-1

Step-by-step explanation:

-5^2 is -25 because you have to do exponents first, so 5^2 is 25. Add a negative symbol there, it becomes -25.

For the denominator, we do the exact same process, except a little different. Since there are parentheses around the negative five, we have to apply the negative symbol on the 5 before we do the exponents. After, we do -5^2 which is 25 because when you are multiplying negative, you always get a positive.

When we are all done with that, we put the numerator over the denominator to get -25/25, which is equivalent to -1.

Answer:

Step-by-step explanation:

Given:

Equations:

Substitute values of b and t into first equation and solve for t:

Find the values of f and b: