Work out
a) 5 3/4 - 2 1/4 b) 7 2/3 + 2 1/5

Please answer will giv brainliest

Answer:

3% of 66.7 is 2.001 or 2.00

18% of 66.7 is 12.006 or 12.01

Caleb has 30 quarters.

What is arithmetic?

Mathematical arithmetic is the study of the properties of the standard operations on numbers, such as addition, subtraction, multiplication, division, exponentiation, and root extraction.

Here, we have

Given: Caleb has 51 coins (nickels, dimes, and quarters) in a jar, totaling $9. He has three more nickels than dimes.

We have to find out how many quarters Caleb has.

Let x be nickel,

y be dimes and

z be quarters

x + y + z = 51.....(1)

1 quartes = 25 cents

1 dimes = 10 cents

1 nickel = 5 cents

Now, the total dollar is $9,

5x/100 + 10y/100 + 25z/100 = 9

5x + 10y + 25z = 900

x + 2y + 5z = 180....(2)

and

y + 3 = x...(3)

Solving equation(1) and (2), we get

From (1)

x + x-3 + z = 51

2x + z = 54....(4)

From (2)

x + 2(x -3) + 5z = 180

3x + 5z = 186...(5)

Now, by solving equations (4) and (5), we get

x = 12

z = 30

Now,

y + 3 = x

y + 3 = 12

y = 9

Hence, Caleb has 30 quarters.

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The solution for x in the equation y = -2cot(3x), restricted to the interval (0, π/3), is x = (1/3) * arctan(1/2), x = (1/3) * arctan(1), and x = (1/3) * arctan(2).

To solve the equation y = -2cot(3x) for x in the interval (0, π/3), we need to find the values of x that satisfy the equation within that interval.

First, let's rewrite the equation using the identity cot(x) = 1/tan(x):

y = -2/tan(3x)

Now, we can take the reciprocal of both sides:

1/y = -tan(3x)/2

Next, we can take the arctangent of both sides to isolate 3x:

arctan(-1/y) = 3x

Now, divide both sides by 3:

x = (1/3) * arctan(-1/y)

Since we are restricted to the interval (0, π/3), we need to make sure that the values of x we obtain from the equation fall within that range.

Let's calculate x using the given equation for different values of y within the interval:

For y = -2, we have:

x = (1/3) * arctan(-1/(-2)) = (1/3) * arctan(1/2)

For y = -1, we have:

x = (1/3) * arctan(-1/(-1)) = (1/3) * arctan(1)

For y = -1/2, we have:

x = (1/3) * arctan(-1/(-1/2)) = (1/3) * arctan(2)

These calculations will give us the corresponding values of x within the specified interval.

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The solution for x in the interval (0, π/3) is:

x = (1/3) * arctan(1/(-2y))

We rewrite the equation using the reciprocal identity for cotangent:

cot(θ) = 1/tan(θ)

y = -2/tan(3x)

We multiply both sides by -1/2:

-2y = 1/tan(3x)

1/(-2y) = tan(3x)

3x = arctan(1/(-2y))

x = (1/3) * arctan(1/(-2y))

In conclusion, reciprocal identities  are described as the reciprocals of the six fundamental trigonometric functions  which are sine, cosine, tangent, secant, cosecant, cotangent.

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The intervals in the solution set are those that make the inequalities 5(x – 2)(x + 4) > 0 true is (-∞, -4) U (2,∞).

Given that,

The inequality is 5(x – 2)(x + 4) > 0

We need to address the inequality and find a solution.

We know that,

Take the inequality

5(x – 2)(x + 4) = 0

Divide the equation both sides by 5

(x – 2)(x + 4) = 0

Now, we take each factor equal to 0

x-2 =0 , so x= 2

x+4 =0, so x= -4

Now we get

First interval (-∞,-4)

Second interval (-4,2)

Third interval (2,∞)

Now,

We take each interval with our inequality

First interval (-∞,-4), pick a number in this interval and check with our inequality.

Lets pick -5

5(-5 – 2)(-5 + 4) > 0

35>0 is true

Second interval (-4,2), pick a number in this interval and check with our inequality.

Lets pick 0

5(0– 2)(0 + 4) > 0

-40>0 is false

Third interval (2,∞), pick a number in this interval and check with our inequality.

Lets pick 3

5(3 – 2)(3 + 4) > 0

35>0 is true

The intervals in the solution set are those that make the inequalities true is (-∞, -4) U (2,∞).

Therefore, The intervals in the solution set are those that make the inequalities 5(x – 2)(x + 4) > 0 true is (-∞, -4) U (2,∞).

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Answer:

B

Step-by-step explanation:

True. Regression analysis involves analyzing the relationship between two variables, typically by using all available data points.

Ignoring certain data points, such as the highest and lowest volume data points, can skew the results and lead to inaccurate conclusions. Therefore, it is important to use all available data points in regression analysis to ensure that the relationship between the variables is accurately represented.

True: Regression analysis uses all data points, not just the highest and lowest volume data points. It is a statistical method for analyzing the relationship between a dependent variable and one or more independent variables. By including all data points, regression analysis can identify patterns and trends, providing a more accurate representation of the data. This allows for better predictions and insights into the relationships between variables. Excluding some data points, such as only using the highest and lowest volume data points, would limit the analysis and potentially lead to inaccurate results.

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Answer:

\(12\) cm

Step-by-step explanation:

If Kelsey knit a total of \(6\) cm of scarf over \(2\) nights, then we know that she can knit \(\frac{6}{2}=3\) cm each night. Therefore, after \(4\) nights of knitting, Kelsey would have knit a total of \(3*4=12\) cm of scarf in total. Hope this helps!

Answer:

95 cents

Step-by-step explanation:

3.80/4 = 0.95

Answer:

The answer is (2, -1)

Step-by-step explanation:

Plug in x and y into the equation:

y=2x-5

-1=2(2)-1

and then u get -1 = -1 which is true

The given equation does not have a unique solution for x as it results in a contradiction. The matrix equation and its corresponding system of linear equations are inconsistent.

First, subtract \(-x^{2}\)  from both sides of the equation to rewrite it as a matrix equation:  \(\left[\begin{array}{ccc}x&1&x\\2&x&3\\x+1&4&x\end{array}\right]\) + \(\left[\begin{array}{ccc}x^{2} &0&0\\0&x^{2} &0\\0&0&x^{2} \end{array}\right]\) = \(\left[\begin{array}{ccc}0&0&0\\0&0&0\\0&0&0\end{array}\right]\).

Simplifying the matrix equation, we have:

\(\left[\begin{array}{ccc}x+x^{2} &1&x\\2&x+x^{2} &3\\x+1&4&x+x^{2} \end{array}\right]\) = \(\left[\begin{array}{ccc}0&0&0\\0&0&0\\0&0&0\end{array}\right]\)

Now, equate the corresponding elements of the matrices and solve the resulting system of equations to find the value(s) of x.

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The 95% confidence interval for μ is [12.2, 16.3].

To calculate the confidence interval for μ, we can follow these steps:

Calculate the sample mean (x¯) and sample standard deviation (s).

The given sample data is: 16, 13, 14, 14.

The sample mean (x¯) is obtained by summing up all the values and dividing by the sample size:

x¯ = (16 + 13 + 14 + 14) / 4 = 57 / 4 = 14.25.

The sample standard deviation (s) is calculated using the formula:

s = SQRT[ Σ(x - x¯)² / (n - 1) ].

Substituting the values:

s = SQRT[ ( (16 - 14.25)² + (13 - 14.25)² + (14 - 14.25)² + (14 - 14.25)² ) / (4 - 1) ]

 = SQRT[ ( 2.0625 + 1.5625 + 0.0625 + 0.0625 ) / 3 ]

 = SQRT[ 3.75 / 3 ]

 ≈ 1.09.

Determine the critical value (t*) for a 95% confidence level.

The critical value depends on the sample size and the desired confidence level. Since the sample size is 4, we have (n - 1) = 3 degrees of freedom. Consulting the t-distribution table or using statistical software, we find that the critical value for a 95% confidence level with 3 degrees of freedom is approximately 2.776.

Calculate the confidence interval.

The confidence interval formula is: Estimate ± Critical Value × Standard Error.

Plugging in the values, we get:

Lower bound = x¯ - t* × s / SQRT(n) = 14.25 - 2.776 × 1.09 / SQRT(4) ≈ 12.2.

Upper bound = x¯ + t* × s / SQRT(n) = 14.25 + 2.776 × 1.09 / SQRT(4) ≈ 16.3.

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Answer: the first table.

Step-by-step explanation:

The terms in the domain (x) should have only one range (y)

Answer:

A) x: -3, 0, -2, 8

    y: -1, 0, -1, 1

Step-by-step explanation:

Function has only one output for each input.

OAmalOHopeO

Answer:

move to the left 3 more spaces

Step-by-step explanation:

you are at -8 already. Therefore, you (-3) more spaces, so you go to the left three more spaces. Use the saying keep change change to help with this.

Keep the first number sign, change the next sign, and the next sign.

Answer:

d

Step-by-step explanation:

Answer:

x = 9.238 y = 4.619

Step-by-step explanation:

I kind of forgot how to do sohcahtoa but we do cosine for one of them. I used a calculator but the lengths seems reasonable so I'm sure they should be right.

When receiving ammunition, unit personnel perform three tasks: ensuring items requested match item numbers on DA Form 3151-R, loading and securing the ammunition, and placarding the vehicle.

The first task performed by unit personnel when receiving ammunition is to ensure that the items requested match the item numbers on DA Form 3151-R. This form serves as a record of the types and quantities of ammunition being received. By comparing the requested items with the item numbers on the form, personnel ensure accuracy and prevent any discrepancies or errors in the delivery.

The second task involves the loading and securing of the ammunition. Unit personnel are responsible for safely and efficiently loading the ammunition onto the designated vehicle or storage area. This includes following proper handling procedures, using appropriate equipment, and adhering to safety protocols. The ammunition must be securely stored and arranged to prevent shifting or damage during transportation.

The final task is to placard the vehicle. Placarding involves visibly displaying the necessary warning signs or labels on the vehicle that indicate the presence of ammunition. This step is crucial for safety and compliance purposes, as it alerts other personnel and drivers to exercise caution when approaching or handling the vehicle. Clear and prominent placarding helps prevent accidents and ensures that everyone involved is aware of the potential hazards associated with transporting ammunition.

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a) We have to identify which values of the set for p satisfy 4p-p < 13.

We can rearrange the inequality to find the value of p:

Then, the values from the set that satisfy 4p - p < 13 are 1, 2, 3 and 4.

b) As the inequality 4p-p > 13 is the complement of the previous inequality (knowing that 4-p = 13 does not match any value in the set), the other values of the set not included in the previous solution will satisfy this equation.

Then, the values from the set that satisfy 4p - p > 13 are 5, 6, 7, 8 and 9.

Answer:

The values of p from {1, 2, 3, 4, 5, 6, 7, 8, 9} that make 4p − p < 13 true are: 1, 2, 3, 4.

The values of p from the set that make 4p − p > 13 true are: 5, 6, 7, 8, 9.

The length of this rectangular room is equal to 9 meters.

The breadth of this rectangular room is equal to 5 meters.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = xy

Where:

If length would become 3 meters less and breadth would become 1 meter more, we have the following expressions;

y = x - 3

x = y + 1

45 = xy

When the rectangle turns to a square, all of the side lengths become equal;

y + 1 = x - 3

x = y + 4

From the area of a rectangle formula, we have:

45 = (y + 4)y

45 = y² + 4y

y² + 4y - 45 = 0

y² + 9y - 5y - 45 = 0

y(y + 9) - 5(y + 9) = 0

y = 5 or -9 meters.

For the length, we have:

x = y + 4

x = 5 + 4

x = 9 meters.

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When the ride accelerates upwards at 3.0 m/s², the scale will show a weight greater than 150 lbs. When the ride accelerates downwards at 3.0 m/s², the scale will show a weight less than 150 lbs. When the ride moves at a constant velocity, the scale will show a weight of 150 lbs.

When the ride accelerates upwards at 3.0 m/s², the scale will show a weight greater than 150 lbs. This is due to the additional force exerted on your body as the ride pushes you upwards. The scale measures the normal force acting on you, which is equal to your weight plus the additional force from the acceleration. As a result, the scale will display a weight higher than your actual weight of 150 lbs.

On the other hand, when the ride accelerates downwards at 3.0 m/s², the scale will show a weight less than 150 lbs. In this case, the acceleration is in the opposite direction to the gravitational force, causing a decrease in the normal force. The scale measures the normal force, which is equal to your weight minus the force due to acceleration. Therefore, the scale will display a weight lower than 150 lbs.

When the ride moves at a constant velocity, the scale will show a weight of 150 lbs. At constant velocity, there is no acceleration acting on your body. The scale measures the normal force, which is equal to your weight. Since there are no additional forces from acceleration, the scale will display your actual weight of 150 lbs.

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(i) there are approximately 266 6 by 6 permutation matrices with det(P) = 1.

(i) The number of 6 by 6 permutation matrices with det(P) = 1 can be determined by counting the number of derangements of a set of size 6. A derangement is a permutation in which no element appears in its original position. The number of derangements of a set of size n is given by the derangement formula:

D(n) = n! * (1/0! - 1/1! + 1/2! - 1/3! + ... + (-1)^n/n!)

For n = 6, the number of derangements is:

D(6) = 6! * (1/0! - 1/1! + 1/2! - 1/3! + 1/4! - 1/5! + 1/6!)

Simplifying the expression:

D(6) = 6! * (1 - 1 + 1/2 - 1/6 + 1/24 - 1/120 + 1/720)

D(6) = 6! * (0.368056)

D(6) ≈ 265.99

(ii) Finding a specific 6 by 6 permutation matrix that requires 4 row exchanges to reach the identity matrix would involve a trial-and-error process or a specific algorithm. It's difficult to provide a specific matrix without additional information or constraints.

(b) Statements:

(i) If det(A - B) = 0 then det(A) = det(B).

False. The determinant of a matrix is not necessarily preserved under subtraction. For example, consider A = [[1, 0], [0, 1]] and B = [[1, 1], [1, 1]]. Here, det(A - B) = det([[0, -1], [-1, 0]]) = 1, but det(A) = det(B) = 1.

(ii) If A is non-singular, then it is row equivalent to the identity matrix.

False. Row equivalence means that two matrices can be transformed into each other through a sequence of elementary row operations. A non-singular matrix, also known as invertible or non-singular, is row equivalent to the identity matrix after a sequence of row operations. However, the statement is not true in general. For example, consider the matrix A = [[1, 2], [2, 4]]. It is non-singular (the determinant is 0), but it is not row equivalent to the identity matrix.

(iii) If A and B are square matrices, then det(A + B) = det(A) + det(B).

False. The determinant of a sum of matrices is not equal to the sum of their determinants. In general, det(A + B) ≠ det(A) + det(B). For example, consider A = [[1, 0], [0, 1]] and B = [[-1, 0], [0, -1]]. Here, det(A + B) = det([[0, 0], [0, 0]]) = 0, while det(A) + det(B) = 2.

(iv) If A is a square matrix of order 3 and det(A) = -4, then det(Aᵀ) = -12.

True. The determinant of the transpose of a matrix is equal to the determinant of the original matrix. Therefore, if det(A) = -4, then det(Aᵀ) = -4. The determinant is unaffected by transposition.

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The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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tried my best to show the steps!! all i did was isolate to find the missing widths attached to the respective lengths (divided surface area by width) and then multiply both sides by two and add them together to find the perimeter.

The dimensions of the garden that would require the least amount of fencing are 6 ft in length and 6 ft in width.

The dimensions are the sides of a geometric shape.

The lengths of the three gardens are given as 6 ft, 9 ft, and 12 ft respectively.

If the area of the garden is 36 feet squared, then the widths for the three lengths will be as follows:

The width of the garden with a length of 6 ft \(= \dfrac{36}{6} = 6\ ft\)

The width of the garden with a length of 9 ft \(= \dfrac{36}{9} = 4\ ft\)

The width of the garden with a length of 6 ft \(= \dfrac{36}{12} = 3\ ft\)

The parameters are calculated as:

The parameter of the garden with dimensions (6 ft, 6 ft) = 2(6 + 6) = 24 ft

The parameter of the garden with dimensions (9 ft, 4 ft) = 2(9 + 4) = 26 ft

The parameter of the garden with dimensions (12 ft, 3 ft) = 2(12 + 3) = 30 ft

The least of the parameter is of the garden with dimensions (6 ft, 6 ft).

Thus, the garden with dimensions (6 ft, 6 ft) would require the least amount of fencing.

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Answer: 99 inches

Step-by-step explanation:

First multiply the whole number by 12 in which you would get 96. Then you would do 1÷4 which equals 0.25 and then multiply by 12 you would get 3. Lastly add them together and you get 99.

Here is the formula: A = ([w • 2] + [{n ÷ d} • ])

Answer:

please continue i'm facinated on were this story goes

Step-by-step explanation:

From the graph, the correct options are given as,
B. Mia left her house 10 minutes before Erick left his house.
D. Erick and Mia arrived at the park at the same time.
E. Erick walked the same distances as Mia during the last 10 minutes.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
The graphs show their distances from home over the same 30-minute period as they walked to the park.
From the graph,
It can be concluded that,
Both reach the park at the same time, as the termination point of the curve is the same.
The graph of mia starts after 10 minutes Erick, which implies Mia left her house 10 minutes before Erick left his house. And Erick walked the same distances as Mia during the last 10 minutes as the slope of the last segment of both curves is the same.

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The probability of drawing three nines in a row from a standard deck of cards without replacement is 1/850 or 0.00118.

The events of drawing a nine and drawing a nine the next time are dependent because the outcome of the first event affects the probability of the second event.

The probability of drawing a nine on the first draw is 4/52 since there are 4 nines in a standard deck of 52 cards).

The probability of drawing a nine on the second draw is 3/51.

The probability of drawing a nine on the third draw is 2/50.

The probability of drawing three nines in a row without replacement is:

(4/52) * (3/51) * (2/50) = 1/850

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Answer: C

Step-by-step explanation:

Answer:

it isn't C or B

it's either A or D

hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

A nonexperimental research design is a type of research design that lacks manipulation of the independent variable and random assignment.

In other words, the researcher does not intervene or manipulate the independent variable, but instead observes and measures it in its natural setting. Nonexperimental designs are often used in observational studies, surveys, and correlational research.

The absence of manipulation of the independent variable is a key feature of nonexperimental designs. Instead, the researcher typically observes and measures the independent variable in its natural setting, along with the dependent variable. This allows the researcher to examine relationships between variables and draw conclusions about their association, but does not allow for causal inferences.

Nonexperimental research designs are useful for investigating naturally occurring phenomena, exploring relationships between variables, and generating hypotheses for further research. However, they are limited in their ability to establish cause-and-effect relationships due to the lack of manipulation and random assignment.

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The two-period moving average model and the two-period weighted moving average model are both common forecasting methods used to predict future demand. and we understand that the model with the lower MAD and MSE values will have the most accurate forecast.

To determine which model is better for this particular data set, we need to compare the accuracy of each model. To do this, we will calculate the Mean Absolute Deviation (MAD) and the Mean Squared Error (MSE) for each model.
For the two-period moving average model, we can calculate the forecast for period 7 by taking the average of p5 and 6:

Period 7 forecast = (Gallons in Period 5 + Gallons in Period 6)/2

For the two-period weighted moving average model, we can calculate the forecast for period 7 by using the weights of 0.6 and 0.4:

Period 7 forecast = (0.6 x Gallons in Period 5) + (0.4 x Gallons in Period 6)

We can then compare the accuracy of each model by calculating the MAD and MSE. To calculate MAD, we need to subtract the actual demand in each period from the forecasted demand and take the absolute value:

MAD = |Actual demand – Forecasted demand|

To calculate MSE, we need to square the differences between the actual demand and the forecasted demand:

MSE = (Actual demand – Forecasted demand)^2

After calculating the MAD and MSE for each model, we can compare the results to determine which model is better for this data set. The model with the lower MAD and MSE values will have the most accurate forecast.

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Answer:

LCM of 5, 10, and 12 is 60

6, 10, and 12 is 60

2, 4, and 9 is 36

Answer:hate math brother

Step-by-step explanation:

Answer:

672

Step-by-step explanation:

We are given that there are a total of 8 Pizza Huts and they sold a total of 5,376 pizzas.  We are asked to find how many pizzas each store sold, so we divide:

5376/8

=672

Each Pizza Hut sold 672 pizzas.

Hope this helps! :)