find the least common denominator of the fractions: 1/7 and 2/3

Answer:

$50.40

Step-by-step explanation:

To find how much Lana will pay in total follow these steps.

First, multiply 40 by 1.05.

40×1.05=42.

This is how much she will pay for the food plus tax.

Now, multiply 42 by 1.2.

42×1.2=50.40

This is how much she will pay for the food, tax, and tip.

Lana will pay a total of $50.40.

Hope this helps!

Answer:

If Sandy spends the whole standard workday sawing, they can saw 3 cords of wood. If they spend the whole day splitting, they can split 5 cords of wood. However, Sandy cannot spend the whole day both sawing and splitting. Therefore, the largest number of cords of wood that Sandy can saw and split in a standard workday is less than or equal to 3 + 5 = 8.

To find the largest number of cords of wood that Sandy can saw and split, we need to find a way to divide the work between sawing and splitting. Let's assume that Sandy spends x fraction of the day sawing and (1-x) fraction of the day splitting. Then, the amount of wood that Sandy can saw in that time is 3x cords, and the amount of wood that Sandy can split in that time is 5(1-x) cords. The total amount of wood that Sandy can saw and split is the sum of these two amounts:

3x + 5(1-x) = 3x + 5 - 5x = 5 - 2x

To maximize this quantity, we need to choose the value of x that makes it as large as possible. Since 0 <= x <= 1, the maximum value of 5 - 2x occurs at x = 0 (Sandy spends the whole day splitting) or x = 1 (Sandy spends the whole day sawing). Therefore, the largest number of cords of wood that Sandy can saw and split in a standard workday is 5 cords, which Sandy can achieve by spending 2/5 of the day sawing and 3/5 of the day splitting.

The statement "if two noncollinear rays join at a common endpoint, then an angle is created" represents the geometry term "angle."

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle.

The two rays are called the sides of an angle, and the common endpoint is called the vertex.

The angle that lies in the plane does not have to be in the Euclidean space.

An angle is formed when two non-collinear rays join at a common endpoint.

This endpoint is called the vertex of the angle.

The two rays are referred to as the arms of the angle.

Angles can be classified according to their degree measurement.

An acute angle measures less than 90 degrees, a right angle measures exactly 90 degrees, and an obtuse angle

measures between 90 and 180 degrees.

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The amount of X and Y that can give Adam the most utility is (αI/ Px) units of good X and (βI/ Py) units of good Y.

The Cobb-Douglas utility function represents a consumer's preferences towards two goods, X and Y. The function for Adam's preferences is given by:

U(x,y)=x α * y β, where α + β = 1. Given the price of good X is Px, the price of good Y is Py, and Adam's disposable income is I.

The total expenditure (E) for two goods will be:

E= PxX + PyY, Where X is the quantity of good X and Y is the quantity of good Y.

Adam's income constraint can be represented as:

I = PxX + PyY

We can rewrite the above expression as:

X = (I/ Px) - ((Py/Px)Y)

Thus, Adam's utility function can be written as:

U = X α * Y β

Substituting X with the expression we derived above, we get:

U = [(I/ Px) - ((Py/Px)Y)] α * Y β

To get the optimal consumption bundle, we need to maximize the utility function, which is given by:

MUx/ Px = α(Y/X)β

Muy/ Py = β(X/Y)α

Multiplying the two equations, we get:

MUx * Muy = αβ

Now, substituting the value of α + β = 1 in the above equation, we get:

MUx * Muy = α(1 - α)

Similarly, dividing the two equations, we get:

MUx / Muy = α/β

Now, we have two equations and two unknowns. We can solve them to get the values of X and Y, which maximize Adam's utility.

After solving, we get:

X = (αI / Px)

Y = (βI / Py)

Thus, the amount of X and Y that can give Adam the most utility is (αI/ Px) units of good X and (βI/ Py) units of good Y.

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The most suitable step to be taken would be to increase the diameter of the pipes (Option C). This would help reduce the frictional losses and allow for a higher flow rate, thus ensuring that the required flow rate is achieved.

As a project engineer, if the produced flow rate (Q) by a pump is less than the required flow rate, several factors need to be considered to determine the appropriate step to take.

Option A) Decrease the diameter of the pipes: Decreasing the pipe diameter would actually result in a higher frictional loss and potentially reduce the flow rate even further. This option would not be suitable in this case.

Option B) Increase the efficiency of the pump: Increasing the pump efficiency would certainly help to optimize the performance and potentially increase the flow rate. This can be achieved through various means such as improving the design, replacing worn-out components, or selecting a more efficient pump. However, it may not be sufficient to fully address the shortfall in the flow rate.

Option C) Increase the diameter of the pipes: Increasing the pipe diameter would result in lower frictional losses and potentially allow for a higher flow rate. This option can be effective in improving the flow rate, especially if the current pipe diameter is a limiting factor.

Option D) Increase the head supplied by the pump: Increasing the head supplied by the pump would not directly impact the flow rate. Head refers to the pressure or energy provided by the pump, which is not directly related to the flow rate.

In conclusion, the most suitable step to be taken would be to increase the diameter of the pipes (Option C). This would help reduce the frictional losses and allow for a higher flow rate, thus ensuring that the required flow rate is achieved.

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The salary of someone working in the industry with a z-score of -1.12 is approximately $43,825.

To find the salary of someone with a specific z-score, we can use the formula:

X = μ + (z * σ),

where X is the salary, μ is the mean annual salary, z is the z-score, and σ is the standard deviation.

Given that the mean annual salary (μ) is $47,581 and the standard deviation (σ) is $3,354, we can substitute these values into the formula:

X = 47,581 + (-1.12 * 3,354).

Performing the calculations, we get:

X ≈ 47,581 - 3,753.48.

Rounding to the nearest dollar, the salary is approximately $43,825. This means that an employee working in the industry whose salary has a z-score of -1.12 earns approximately $43,825 per year. The negative z-score indicates that the salary is below the mean, as expected since the z-score is negative.

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When a sample is taken from a population, it is important to understand the characteristics of both the sample and the population. In this scenario, the sample size is 36, meaning that 36 individuals or data points were randomly selected from the larger population.

The population mean is 50, which tells us the average value of the population data. The standard deviation of the population is 5, which indicates the degree of variability in the data.

Using the information provided, we can calculate the standard error of the mean (SEM), which is the standard deviation of the sample mean. The formula for SEM is:

\(SEM = population standard deviation / square root of sample size\)

SEM = 5 / square root of 36

SEM = 5 / 6

SEM = 0.83

Therefore, the standard error of the mean for this sample is 0.83. This means that if we were to take many samples of size 36 from this population, we would expect the mean of each sample to be within 0.83 units of the true population mean of 50.

It is important to note that while this sample may give us some insight into the characteristics of the larger population, it is not necessarily representative of the entire population. To increase the accuracy of our findings, we would need to take multiple random samples and calculate the means and standard errors of each sample.

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The factored form of an equation is done by rewriting the equation in simpler forms.

The completely factored form of \(8x^2 - 50\) is \(2(2x-5)(2x + 5)\)

The expression is given as:

\(8x^2 - 50\)

Factor out 2 from the expression, \(8x^2 - 50\)

\(8x^2 - 50 = 2(4x^2-25)\)

Express 25 as 5^2

\(8x^2 - 50 = 2(4x^2-5^2)\)

Express 4 as 2^2

\(8x^2 - 50 = 2(2^2x^2-5^2)\)

Rewrite the expression as:

\(8x^2 - 50 = 2((2x)^2-5^2)\)

Express the expression as a difference of two squares

\(8x^2 - 50 = 2(2x-5)(2x + 5)\)

Hence, the completely factored form of \(8x^2 - 50\) is \(2(2x-5)(2x + 5)\)

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.Explanation

The question gives us an exponential equation and asked that we determine the growth rate

Growth rates refer to the percentage change of a specific variable within a specific time period

From the given expression:

If we are to deduce the growth rate, then we will have to compare it with the general formula

The growth factor is the factor by which a quantity multiplies itself over time. The growth rate is the addend by which a quantity increases (or decreases) over time

Thus, in our case

Thus

Hence, the growth rate is 0.03

Because the account increases by 0.03 overtime

The answer is 0.03

Answer:

(2a-7)(2a-7) can be expanded using the FOIL method (First, Outer, Inner, Last):

Step-by-step explanation:

First: (2a)(2a) = 4a^2

Outer: (2a)(-7) = -14a

Inner: (-7)(2a) = -14a

Last: (-7)(-7) = 49

Combining these terms, we have:

(2a-7)(2a-7) = 4a^2 - 14a - 14a + 49

Simplifying further:

= 4a^2 - 28a + 49

Answer:

4a² - 28a + 49

Step-by-step explanation:

Either use FOIL or (a + b)² = a² + 2ab + b²

Using FOIL:

(2a - 7)(2a - 7) = 4a² - 14a - 14a + 49 = 4a² - 28a + 49

Using (a + b)² = a² + 2ab + b²:

(2a - 7)(2a - 7) = (2a - 7)² = 4a² - 28a + 49

Answer:

I think it's B

Step-by-step explanation:

x = -2

2 + x > -8

2 + -2 > -8

0 > -8

The speed of the boat in still water is 8 miles per hour.

Let's call the speed of the boat in still water "x" (in miles per hour).

When Mackenzie rows downstream, the current is helping her, so the effective speed of the boat is (x + 4) miles per hour. The distance traveled is 96 miles. We can use the formula:

distance = rate × time

to set up an equation for the downstream trip:

96 = (x + 4) t

where "t" is the time (in hours) it takes for the downstream trip.

For the upstream trip, the current is working against Mackenzie, so the effective speed of the boat is (x - 4) miles per hour. The distance traveled is still 96 miles, but this time the trip takes 16 hours longer than the downstream trip. So we can set up another equation:

96 = (x - 4) (t + 16)

Now we have two equations with two unknowns (x and t). We can solve for t in the first equation and substitute into the second equation:

96 = (x - 4) (t + 16)

96 = (x - 4) (96/(x + 4) + 16)

Simplifying, we get:

96 = (x - 4) (96/(x + 4) + 16)

96 = 96(x - 4)/(x + 4) + 16(x - 4)

96(x + 4) = 96(x - 4) + 16(x + 4)(x - 4)

96x + 384 = 96x - 384 + 16(x^2 - 16)

96x + 384 = 96x - 384 + 16x^2 - 256

16x^2 = 256 + 384 + 384

16x^2 = 1024

x^2 = 64

x = 8

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Answer:

y=-5x+4

Step-by-step explanation:

Since the 2 equations have to be parallel, the slope is the same. Just substitute the x-value into the slope, and figure out the y. So therefore the answer is y=-5x+4.

For all invertible n×n matrices a and b, the formula ABA^-1 = B holds, while the formula (I-A)(I+A) = I - A^2 does not hold in general.

The formula ABA^-1 = B holds for all invertible n×n matrices a and b. When we multiply a matrix by its inverse and then multiply the result by the original matrix, the intermediate multiplication by the inverse effectively cancels out the original matrix's effect. Therefore, the resulting matrix is simply the second matrix, b. This property holds true for any invertible matrices a and b, regardless of their size.

On the other hand, the formula (I-A)(I+A) = I - A^2 does not hold in general. Here, I represents the identity matrix. While this formula might hold for specific matrices a, it is not universally valid for all invertible n×n matrices. In general, the product of (I-A)(I+A) will not simplify to I - A^2. The difference between the two sides of the equation is the term A^2, which does not always cancel out in this case. Therefore, we cannot conclude that this formula holds for all invertible n×n matrices a.

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Answer:

18. d

19. c (not sure)

20. c

Answer:

18) d. Synopsis

19) c. Duration

20) c. Pacify

Step-by-step explanation:

18) When you don’t wanna give the full version of a story sum it up; give a summary or synopsis!

19) Uh tbh it just makes the most sense in context of the sentence, read it all together and you’ll see ;)

20) In the sentence it says “calm down” only way to calm someone down is to pacify them or give them what they want… in this context she needs to pacify them. Plus it just makes sense.

Hope this helps, good luck have a good day!

Approximately 204.11 years ago, your great, great, great, great grandmother left you $2 in a bank account that has grown to $150,000 today.

To calculate the number of years, we can use the compound interest formula:

\(A = P(1 + r/n)^ {nt}\)

where A is the final amount, P is the principal amount, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

Given that the principal amount is $2, the final amount is $150,000, the annual interest rate is 5.5% (0.055 as a decimal), and the interest is compounded weekly (n = 52), we can solve for t:

\(50,000 = 2(1 + 0.055/52)^{52t}\)

Dividing both sides by $2 and isolating the exponent, we get:

\(75,000 = (1.0010576923076923)^{52t}\)

Taking the logarithm of both sides, we have:

\(log(75,000) = log(1.0010576923076923)^{52t}\)

Using logarithm properties, we can rewrite the equation as:

log(75,000) = 52t * log(1.0010576923076923)

Solving for t by dividing both sides by 52 * log(1.0010576923076923), we find:

t ≈ 204.11 years

Therefore, approximately 204.11 years ago, your great, great, great, great grandmother left you $2 in the bank account.

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Answer:

13

Step-by-step explanation:

42 / 2 = 21

21 - 8 = 13

The postfix expression of "7+5-3*2(6*7)/4" is "7 5 + 3 2 * 6 7 * 2 * - 4 /". Evaluating the postfix expression gives the result of the expression. The prefix expression for the given infix expression is "/ - + 7 5 * 3 * 2 ( * 6 7 ) 4".

To convert the infix expression "7+5-3*2(6*7)/4" into postfix expression, we follow the rules of operator precedence and associativity. The postfix expression is obtained by placing operators after their operands.

The postfix expression for the given infix expression is:

"7 5 + 3 2 * 6 7 * 2 * - 4 /"

To evaluate the postfix expression, we use a stack data structure. We scan the postfix expression from left to right and perform the corresponding operations.

Starting with an empty stack, we encounter the operands "7" and "5". We push them onto the stack. Then we encounter the operator "+", so we pop the last two operands from the stack (5 and 7), perform the addition operation (7 + 5 = 12), and push the result back onto the stack.

We continue this process for the remaining operators and operands in the postfix expression. Finally, after evaluating the entire expression, the result left on the stack is the final answer.

To convert the infix expression into prefix expression, we follow similar rules but scan the expression from right to left. The prefix expression is obtained by placing operators before their operands.

The prefix expression for the given infix expression is:

"/ - + 7 5 * 3 * 2 ( * 6 7 ) 4"

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Answer:

53=-3+14d

56=14d

d=4 that is the common difference

sample response: The pre-image is the point you start with. To check the transformation rule, substitute the values of the coordinates (4, 5) into the rule. You get (4, 5) → (4+4, 5+7). Simplify to get (4, 5) → (8, 12). This is the image. Instead the rule was applied to the image. This is the source of the error.

Answer:

The transformation rule should be applied to the pre-image.  The application of the rule results in the point (8, 12).  The transformation rule was applied to the wrong point.

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Step 1: Plug in the values.

Step 2: Multiply 3 by 5.

Step 3: Subtract 5 from 15.

Therefore, f(5) = 10.

Answer:

f(5) = 10

Step-by-step explanation:

f(x) means that x is put into the variable on the right.

f(5) means that 5 is put into the variable on the right. So you put a 5 in where you see an x on the right.

f(5) = 3*5 - 5

f(5) = 15 - 5

f(5) = 10

There are different values of t_crit (critical value of t) when samples have different sample sizes because the critical value depends on both the level of significance (alpha) and the degrees of freedom (df), and the df is calculated differently for different sample sizes.

When calculating the t_crit value, the level of significance (alpha) is fixed, but the degrees of freedom (df) depend on the sample size. The df represents the number of independent observations in the sample, and it affects the t-distribution curve. As the sample size increases, the df also increases, and the t-distribution curve approaches the standard normal distribution curve. Therefore, for smaller sample sizes, the t_crit value will be larger than for larger sample sizes, since the t-distribution curve is wider and has more variability. This is why different sample sizes require different t_crit values.

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Answer:

set everything equal to itself, like for #3 do 7x+14=9x-2 and solve for x, the same goes for the first two

Step-by-step explanation:

follow my insta anthony.cb8

Answer:

63

Step-by-step explanation:

1/4 of 168 is 42 which is how many Boxes of Candy they sold

42 x 1.50 = 63

Answer:

From the sale of boxes of candy, the team made $63

Explanation:

We know that 3/4 of the sold items were chocolate bars. A fast trick to find 3/4ths, or 75%, of a number is to multiply it by 3 and divide by 4.

168 * 3 = 504

504 ÷ 4 = 126

Now, we do 168 - 126 to find the number of candy boxes.

168 - 126 = 42

So, the soccer team sold 42 boxes of candy. Since each box was $1.50, we just multiply

42 * 1.50 = 63

The soccer team made $63 dollars by selling candy boxes.

Note: This is just my way that I did quickly, there are many many other ways to do this. Try to find what's best for you.

Answer:

x should equal 16

Step-by-step explanation:

The option that follows is c .

The between-group estimate for calculating the degrees of freedom in ANOVA is calculated using the formula k - 1, where k represents the number of groups or treatments being compared.

This estimate represents the variability between the group means and is used in the F-ratio calculation to determine if the differences between the groups are significant.

When conducting ANOVA, the between-group estimate is an important factor in determining the degrees of freedom. This estimate represents the variability between the group means and is used to calculate the F-ratio, which determines if the differences between the groups are significant. The between-group estimate is calculated using the formula k - 1, where k represents the number of groups being compared. This formula is used because the estimate is based on the number of independent sources of variation between the groups. By accurately calculating the degrees of freedom, researchers can determine if the differences between the groups are statistically significant.

The between-group estimate for calculating the degrees of freedom in ANOVA is crucial for determining the statistical significance of differences between groups. It is calculated using the formula k - 1, where k represents the number of groups being compared. This estimate represents the variability between the group means and is used in the F-ratio calculation. Accurately calculating the degrees of freedom is essential in conducting valid ANOVA analyses.

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The height of the average Sandwich tern is,

⇒ 2 + r

We have,

Scientists are studying different types of birds called terns.

The height of the average Sandwich tern is 2 inches more than the height of the average Roseate tern.

Let us assume that,

The height of the Roseate tern = r

Hence, We can formulate,

The height of the average Sandwich tern is,

⇒ 2 + r

Therefore, The height of the average Sandwich tern is,

⇒ 2 + r

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Answer:

9/10, 0.9, 90%

Step-by-step explanation:

0.900 x 1000

1 x 1000= 9 over 10

0.9 just take the two 0s off the end

and to get percent move the decimal to places over to the right. Hope this helped!

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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