At the age of 14, Lois was 5 foot 3 inches tall. After hitting a growth spurt, at the age of 16, Lois was 5 foot 11 inches tall. What is the percent of increase in Lois' height over that time?​

The days for Connor's and Adam's birthday are given as: Connor’s birthday is the first one in September and is 16 days before the second birthday. Adam has the second birthday. Their birthday day numbers add up to 30. Therefore, to find the days for Connor's and Adam's birthdays.

we need to perform the following steps Let’s assume that Connor’s birthday is on the xth of September. Then Adam's birthday is on the 16th + xth of September. Their birthday day numbers add up to 30. Thus, x + (x + 16) = 30Simplify the equation: 2x + 16 = 30We have to isolate the variable, x. Subtract 16 from both sides: 2x = 14x = 7Therefore, Connor's birthday is on the 7th of September, and Adam's birthday is on the 16th + 7 = 23rd of September.

Let’s assume that Connor’s birthday is on the xth of September. Then Adam's birthday is on the 16th + xth of September. Their birthday day numbers add up to 30. Thus, x + (x + 16) = 30Simplify the equation: 2x + 16 = 30We have to isolate the variable, x. Subtract 16 from both sides: 2x = 14x = 7 Therefore, Connor's birthday is on the 7th of September, and Adam's birthday is on the 16th + 7 = 23rd of September. Therefore, Connor's and Adam's birthday days are September 7th and September 23rd, respectively.

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Answer:

JK = 3\(\sqrt{3}\)

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos60° = \(\frac{1}{2}\) , then

cos60° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{JK}{JL}\) = \(\frac{JK}{6\sqrt{3} }\) = \(\frac{1}{2}\) ( cross- multiply )

2JK = 6\(\sqrt{3}\) ( divide both sides by 2 )

JK = 3\(\sqrt{3}\)

Answer: 16

to find the mean you have to add all the numbers up and divide it by how many numbers are in the set

Answer:

\( \frac{10 + 5 + 7 + 14 + 19 + 32 + 25}{7} \\ = 16\)

Let's begin by identifying key information given to us:

To obtain the angle C, we will use the Law of Cosines as shown below:

The rocket's height when the distance between you and the rocket is 100 feet is 98.9 feet

The function is given as:

d = √216 +h²

At a distance of 100 feet, it means that:

d = 100

So, we have:

√216 +h² = 100

Take the square of both sides

216 +h² = 10000

Subtract 216 from both sides

h²= 9784

Take the square root of both sides

h = 98.9

Hence, the rocket's height when the distance between you and the rocket is 100 feet is 98.9 feet

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Answer:

-8.72

Step-by-step explanation:

The age of Jeremy could be less than 22 years

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

Jeremy = Rachel - 2

Let Jeremy = x and Rachel = y

So, we have

y = y - 2

Their ages added together is less than 46

So, we have

x + y < 46

This gives

x + x + 2 < 46

So, we have

2x < 44

Divide

x < 22

Hence, Jeremy could be less than 22 years

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Question

Jeremy is two years older than Rachel. The sum of the ages of Jeremy and Rachel is less than 46

How old could Jeremy be?

Answer:

1400 divided by 50 = 28 boxes

Step-by-step explanation:

50 times 28 = 1400

For n = 421, find its square root: √421 ≈ 20.52. There are 8 prime numbers less than or equal to 20.52: 2, 3, 5, 7, 11, 13, 17, and 19. Testing for divisibility, 421 is not divisible by any of these prime numbers, so n = 421 is prime.

To test whether 323 is prime, we need to find the prime numbers less than or equal to its square root. The square root of 323 is approximately 17.97, so we need to find the prime numbers less than or equal to 17. The prime numbers less than or equal to 17 are 2, 3, 5, 7, 11, 13, and 17. We can check whether 323 is divisible by any of these numbers. If it is not divisible by any of them, then it is prime.

323 is divisible by 17, so it is not prime.

To test whether 421 is prime, we need to find the prime numbers less than or equal to its square root. The square root of 421 is approximately 20.52, so we need to find the prime numbers less than or equal to 20. The prime numbers less than or equal to 20 are 2, 3, 5, 7, 11, 13, 17, and 19. We can check whether 421 is divisible by any of these numbers. If it is not divisible by any of them, then it is prime.

421 is not divisible by any of these numbers, so it is prime.
For n = 323, first find its square root: √323 ≈ 17.97. There are 7 prime numbers less than or equal to 17.97: 2, 3, 5, 7, 11, 13, and 17. Testing for divisibility, 323 is divisible by 17 (323 = 17 * 19), so n = 323 is not prime.

For n = 421, find its square root: √421 ≈ 20.52. There are 8 prime numbers less than or equal to 20.52: 2, 3, 5, 7, 11, 13, 17, and 19. Testing for divisibility, 421 is not divisible by any of these prime numbers, so n = 421 is prime.

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It is important to note that continuous random variables typically represent measured data, such as the weight or height of an individual, while discrete random variables typically represent counted data, such as the number of heads in a series of coin flips.

The mean of a probability distribution, also known as the expected value, is a measure of central tendency that represents the average value of a random variable in the long run. It is calculated by taking the weighted average of all possible values that the random variable can take, with the weights being the probabilities of each value occurring.

In the case of a discrete random variable, the mean is calculated by multiplying each possible value by its probability and then summing the results. For a continuous random variable, the mean is calculated by integrating the product of the value and its probability density function over the entire range of possible values.

The mean is significant because it provides a measure of the central tendency of a probability distribution, which can be used to make predictions about future outcomes. It is also used in various applications, such as calculating the expected value of a financial investment or the expected number of occurrences of an event in a given time period.

It is important to note that continuous random variables typically represent measured data, such as the weight or height of an individual, while discrete random variables typically represent counted data, such as the number of heads in a series of coin flips.

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Answer:

x=4

Step-by-step explanation:

Add 4 to both sides.

12x=5x+24+4

Simplify  5x+24+4 to  5x+28

Subtract 5x from both sides

12x-5x=28

Simplify  12x-5x1 to 7x

7x=28

Divide both sides by 7

28/7

simplify 28/7

x=4

Answer:

4

Step-by-step explanation:

12x - 4 = 5x + 24 convert like terms to the same side of equation

12x - 5x = 24 + 4 as you can see, when we send a terms to the other side of equation its sign changes

7x = 28 multiply both sides by 7

x = 4

x² + 6x + 5 = 0

To find the solution, we can use the quadratic formula.

The solutions are (-1, 0) and (-5, 0)

First you will get 4dz

Answer:

e) 17 miles

Step-by-step explanation:

15^2+8^2=289

\(\sqrt{289\)=17

Answer:

=47/36

(Decimal: 1.305556)

Step-by-step explanation:

Answer:

3 1/4

Step-by-step explanation:

3/4 + ( 1/3 / 1/6 ) - (- 1/2)

First, divide within the parenthesis

3/4 + 2 - (- 1/2)

Next, change the double subtraction to an addition

3/4 + 2 + 1/2

Convert to forths

3/4 + 2 + 2/4

Add 3/4 and 2

2 3/4 + 2/4

Add 2 3/4 and 2/4

3 1/4

I hope that this helps :)

Answer: The person above me is correct. Here is a picture if you still dont get it..

Step-by-step explanation:

Answer:

2 eggs

Step-by-step explanation:

Mean is average, so add all the numbers together then divide by how many numbers there are.

3 + 3 + 2+ 3 + 1 + 2 + 1 + 1 = 16

16 ÷ 8 = 2

The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

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The minimum value of the function is 2(-√(8/5)) + 3(-√(9/5)) = -3.6, and the maximum value is 2(√(8/5)) + 3(√(9/5)) = 3.6.

The minimum and maximum values of the function f(x, y) = 2x + 3y with constraint x² + y² = 4 can be found using the Lagrange multiplier method.

To find the minimum and maximum values of the function f(x, y) = 2x + 3y subject to the constraint x² + y² = 4, you need to use the Lagrange multiplier method. The steps are as follows:

1. Define the function f(x, y) = 2x + 3y and constraint g(x, y) = x² + y² - 4.
2. Compute the gradients of both functions: ∇f(x, y) = (2, 3) and ∇g(x, y) = (2x, 2y).
3. Set up the Lagrange multiplier equation: ∇f(x, y) = λ∇g(x, y), so (2, 3) = λ(2x, 2y).
4. Solve the system of equations: 2 = 2λx, 3 = 2λy, and x² + y² = 4.

From solving, we find two solutions: (x, y) = (±√(8/5), ±√(9/5)).

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Complete question:

find the minimum and maximum values of the func- tion subject to the given constraint. (x, y) = 2x + 3y, x² + y² = 4

Evaluating the piecewise function we get:

h(-2) =-2

h(-0.5) = -1

h(1) = 1

Here we have a piecewise function h(x), where piecewise means that the function has different behaviors in different parts of its domain.

First, we want to find h(-2)

x = -2 is the lower limit of the first part of the function:

h(x) = -2    if -2 ≤ x < -1

Then:

h(-2) = -2

The second value is -0.5, it belongs to the second piece, then:

h(-0.5) = -1

Finally, x = 1 belongs to the last piece of the function, so:

h(1) = 1

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The total amount expected to be deposited in the restaurant's bank account during the month of January from cash, credit card, and debit card sales is equal to the total sales revenue, which is $X.

Cash sales: 40%

Credit card sales: 40%

Debit card sales: 20%

Requirement 1: How much of the total sales revenue is expected to be paid in cash?

Assuming the total sales revenue for January is $X, the amount expected to be paid in cash is 40% of X.

Cash sales = 0.4 × X

Requirement 2: How many customer transactions does the company expect in January?

The number of customer transactions can vary, and the information provided doesn't specify a particular value. You would need to have additional data or assumptions to determine the number of transactions.

Requirement 3: How much of the total sales revenue is expected to be paid with credit cards?

Assuming the total sales revenue for January is $X, the amount expected to be paid with credit cards is 40% of X.

Credit card sales = 0.4 × X

Requirement 4: How many customer transactions will be paid for by customers using credit cards?

Similar to Requirement 2, the number of customer transactions paid for by credit cards would require additional data or assumptions to determine.

Requirement 5: When budgeting for January's operating expenses, how much should the restaurant expect to incur in credit card transaction fees?

To calculate the credit card transaction fees, we need to consider two components: a fixed fee per transaction and a percentage fee based on the amount charged.

Assuming the number of credit card transactions is Y, and the average amount charged per transaction is Z, the credit card transaction fees can be calculated as:

Credit card transaction fees = (0.50 × Y) + (0.02 × Z × Y)

Requirement 6: How much of the total sales revenue is expected to be paid with debit cards?

Assuming the total sales revenue for January is $X, the amount expected to be paid with debit cards is 20% of X.

Debit card sales = 0.2 × X

Requirement 7: How many customer transactions will be paid for by customers using debit cards?

Similar to Requirement 2 and Requirement 4, the number of customer transactions paid for by debit cards would require additional data or assumptions to determine.

Requirement 8: When budgeting for January's operating expenses, how much should the restaurant expect to incur in debit card transaction fees?

Similar to Requirement 5, the debit card transaction fees can be calculated using the same formula but with different values for the fixed fee per transaction and the percentage fee based on the amount charged.

Requirement 10: What is the total amount of money that the restaurant expects to deposit in its bank account during the month of January from cash, credit card, and debit card sales?

Assuming the total sales revenue for January is $X, the total amount expected to be deposited in the bank account is the sum of cash sales, credit card sales, and debit card sales.

Total deposits = Cash sales + Credit card sales + Debit card sales

= 0.4 × X + 0.4 × X + 0.2 × X

= X

Therefore, the total amount expected to be deposited in the restaurant's bank account during the month of January from cash, credit card, and debit card sales is equal to the total sales revenue, which is $X.

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Answer:

22

Step-by-step explanation:

The centroid divides a median in two parts that have this ratio = 1/3 and 2/3

In particular the part between the vertex and the centroid is 2/3 of the median.

So we have:

XN = (33 * 2)/3 = 22

Answer:

hold on what I can't see that sorry it's really blur

dx/dt = 4+3√3 in the case of the circle with radius 4 and the equation x²+y²=16.

The method of finding an implicit function's dependent variable's derivative by differentiating each term individually, symbolizing the derivative, and then solving the resulting expression for the symbol.

Without having to solve the provided equation for y, you may use the implicit differentiation technique to determine the derivative of y with respect to x.

Because we assume that y may be written as a function of x, the chain rule must always be applied when differentiating the function y.

So, the dx/dt will be:

The circle's equation is: x² + y² = 16

Assuming that x = 2, then:

2² + y²   = 16

y² = 12

y = ±√12

Hence, the first quadrant is positive:

y = √12

y = 2√3

When implicit differentiation is used, we get that:

2x dx/dt + 2y dy/dt = 16

If fracdydt = -3, as is the case, then

2(2) dx/dt - 12√3 = 16

4 dx/dt = 16 + 12√3

dx/dt = 16+12√3/4

dx/dt = 4+3√3

Therefore, dx/dt = 4+3√3 in the case of the circle with radius 4 and the equation x² + y² = 16.

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The confidence interval for the given standard deviation is  [992.3, 1390.9].

What is standard deviation?

Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.

Main body:

A)

Mean = 1191.6

standard deviation = 506.6

n = 43

for true average lifetime C.I. = 99%

z value for 99% in z table = 2.55

C.I. = Mean ± z*s/√n

C.I. = 1191.6 ± 2.55*506.6/√43

C.I. = 1191.6 ± 197.0

C.I. = [992.3, 1390.9]

hence the confidence interval  is  [992.3, 1390.9].

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The monthly interest rate you will be paying is approximately $2,583.33, and (b) the alternative loan is less attractive than the one from the car dealer, with the lender needing to charge an interest rate of approximately 2.31% to match the car dealer's rate.

(a) Calculation of the interest rate you will be paying every month:

Given:

The car will cost = $150,000

Amount to be paid upfront = 40%

Interest rate per annum = 2%

Loan tenure (no of years) = 5 years

Loan tenure (no of months) = 5 x 12 = 60 months

Using the formula to calculate the interest rate you will be paying every month:

Interest Rate = (Loan amount x interest rate per annum x Loan tenure (no of years) + loan amount) / Loan tenure (no of months)

Substituting the given values in the formula:

Interest Rate = (150000 x 2 x 5 / 100 + 150000) / 60

Interest Rate = (15000 + 150000) / 60

Interest Rate ≈ $2,583.33

Therefore, the interest rate that you will be paying every month is approximately $2,583.33.

(b) (i) You are able to secure financing for your car from another source. You will have to pay 3% per annum on this loan. The lender requires you to pay monthly for 5 years. Is this loan more attractive than the one from the car dealer?

Given:

Interest rate per annum = 3%

Loan tenure (no of years) = 5 years

Loan tenure (no of months) = 5 x 12 = 60 months

Using the formula to calculate the interest rate you will be paying every month:

Interest Rate = (Loan amount x interest rate per annum x Loan tenure (no of years) + loan amount) / Loan tenure (no of months)

Substituting the given values in the formula:

Interest Rate = (150000 x 3 x 5 / 100 + 150000) / 60

Interest Rate = (22500 + 150000) / 60

Interest Rate ≈ $2,916.67

The monthly payment amount is higher than the car dealer's, so this loan is not more attractive than the one from the car dealer.

(ii) Suppose the lender requires you to set aside $10,000 as security to be deposited with the lender until the loan matures and repayment is made. What interest rate must the lender charge for it to be equivalent to the interest rate charged by the car dealer?

Let x be the interest rate that the lender must charge.

Using the formula of compound interest, we can find the interest charged by the lender as follows:

150000(1 + x/12)^(60) - 10000 = 150000(1 + 0.02/12)^(60)

150000(1 + x/12)^(60) = 150000(1.0016667)^(60) + 10000

(1 + x/12)^(60) = (1.0016667)^(60) + 10000/150000

(1 + x/12)^(60) = (1.0016667)^(60) + 0.066667

Taking the natural logarithm on both sides:

60(x/12) = ln[(1.0016667)^(60) + 0.066667]

x ≈ 2.31%

Thus, the lender must charge approximately a 2.31% interest rate to be equivalent to the interest rate charged by the car dealer.

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Answer:

8 Gallons Per Minute

Step-by-step explanation:

Therefore, the line passes through all points whose coordinates have a y-coordinate of -6. For example, the point (0, -6) and the point (10, -6) both lie on this line.

Coordinates are two numbers (Cartesian coordinates), or sometimes a letter and a number, that locate a specific point on a grid, known as a coordinate plane. A coordinate plane has four quadrants and two axes: the x axis (horizontal) and y axis (vertical).

To determine which other coordinate the horizontal line passes through, we need more information about the line. Specifically, we need to know its equation.

A horizontal line has an equation of the form y = c, where c is a constant. Since the line passes through the point (5, -6), we know that -6 is the y-coordinate of this point. Therefore, the equation of the line passing through (5, -6) is y = -6.

Any point that lies on this line must have a y-coordinate of -6. Therefore, the line passes through all points whose coordinates have a y-coordinate of -6. For example, the point (0, -6) and the point (10, -6) both lie on this line.

the point (0, -6) and the point (10, -6) both lie on this line.

Complete question : A horizontal line passes through the coordinates (5, -6). Which of the following coordinate does the line also passes through?

(0, -6) and (10 , -6).

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Answer:

-1,3

Step-by-step explanation:

I just did it don't know how to explain it