A deli has two platters of sandwiches. The first platter costs ​$46 and you get 2 ham sandwiches and 5 roast beef sandwiches. The other platter costs ​$58 and you get 5 ham sandwiches and 3 roast beef sandwiches. What is the cost of each​ sandwich?

You need to manipulate the equations to get the same coefficient for one of the variables and then add or subtract the equations to eliminate that variable.

When using the method of elimination to solve the system of equations, the goal is to eliminate one of the variables by adding or subtracting the equations. To do this, you want to choose a coefficient for one of the variables that is the same in both equations, but with opposite signs.

For example, if the system of equations is:

2x + 3y = 7
4x - 5y = -13

You could multiply the first equation by -2 to get:

-4x - 6y = -14

Then, when you add this equation to the second equation, the x variable is eliminated:

-4x - 6y + 4x - 5y = -14 - 13

Simplifying this equation gives you:

-11y = -27

To find the value of y, you would divide both sides by -11:

y = 27/11

To find the value of x, you would substitute this value of y into one of the original equations and solve for x.

As for the specific question of what is the result of adding the two equations together, it depends on the coefficients of the variables in the equations. You need to manipulate the equations to get the same coefficient for one of the variables and then add or subtract the equations to eliminate that variable.

It looks like you didn't provide the system of equations you need help with. Please provide the two equations, and I'll gladly help you with the method of elimination and the result of adding them together.

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The probability of a student spending time reading given that the student spends time watching TV is  \(P(Reading|Watching\:\:TV)=0.12\)

If any two occurrences in sample space S, A and B, are specified, then the conditional probability of event A given B is:

\(P(A|B)=\frac{P(A\:and\:B)}{P(B)}\)

Probability theory is an important branch of mathematics that is used to model and analyze uncertain events in various fields, including science, engineering, finance, and social sciences. The concept of probability is based on the idea of random experiments, where the outcomes are uncertain and can vary each time the experiment is performed.

The probability of an event can be determined by analyzing the possible outcomes of the experiment and assigning a probability to each outcome based on the assumptions of the model. The theory of probability has several applications in real life, such as predicting the outcomes of games of chance, evaluating risks in insurance and finance, and making decisions in scientific research.

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The most common error when entering a formula is to reference the wrong cell in the formula.

This error occurs when the cell references within a formula do not match the intended cells. It can lead to incorrect calculations and produce unexpected results. For example, if a formula is supposed to use data from cell A1 but mistakenly refers to cell B1, the calculation will be based on the wrong data. It is important to double-check and ensure that the cell references in a formula accurately reflect the intended data sources to avoid this common mistake.

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The angle of elevation is approximately 36.87 degrees.

The tangent function can be used to determine the angle of elevation. We'll abbreviate the distance "d" between the object and the spot where the shadow meets the ground.

Then, we have:

tan(θ) = shadow length / d

tan(θ) = 3 / 4

Solving for θ, we have:

θ = \(tan^-1(\frac{3}{4})\)

The tangent function can be used to calculate the elevation angle. We'll refer to this distance as "d" from the item to the point where the shadow lands on the ground.

θ (degrees) = θ (radians) * 180 / π

Approximating, we have:

θ (degrees) =  \(tan^-1(\frac{3}{4})\) * 180 / π

θ (degrees) ≈ 36.87 degrees

So, the angle of elevation is approximately 36.87 degrees.

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The statements that are true here are statements A and statement C

A. The distance from the hook to the lake's surface is less than the distance from the fisherman's hand to the lake's surface. (True)

The distance from the hook to the lake's surface is 30 feet (depth of the lake), which is greater than the distance from the fisherman's hand to the lake's surface, which is 10 feet.

B. The distance from the fisherman's hand to the hook is the same as the distance from the lake's surface to the lake's bottom. (False)

The distance from the fisherman's hand to the hook is 10 - (-30) = 40 feet, while the distance from the lake's surface to the lake's bottom is 0 - (-30) = 30 feet. Therefore, the distances are not the same.

C. The distance from the fisherman's hand to the lake's surface is less than the distance from the lake's surface to the lake's bottom. (True)

The distance from the fisherman's hand to the lake's surface is 10 feet, which is less than the distance from the lake's surface to the lake's bottom, which is 30 feet.

D. The distance from the lake's surface to the hook is greater than the distance from the lake's bottom to the lake's surface. (False)

The distance from the lake's surface to the hook is 30 feet, while the distance from the lake's bottom to the lake's surface is also 30 feet. Therefore, the distances are the same.

E. When the hook rises 10 feet, the distance from the hook to the lake's surface is the same as the distance from the fisherman's hand to the lake's surface. (False)

If the hook rises 10 feet, its distance from the lake's surface would be 30 - 10 = 20 feet. The distance from the fisherman's hand to the lake's surface would still be 10 feet. Therefore, the distances are not the same.

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The new coordinates of A would be (3, -2)

Answer:

A prime = (3,-2)

x=3

y=-2

Answer:

the item now costs $63.21

\(\huge\text{Hey there!}\)

\(\mathsf{2x^2}\\\\\mathsf{= 2(5)^2}\\\\\mathsf{= 2(5\times5)}\\\\\mathsf{= 2(25)}\\\\\mathsf{= 50}\\\\\\\huge\text{Thus, your answer is: \boxed{\mathsf{50}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

The correct answer is the value x such that: P(X ≥ x) = 0.95

(a) The sum of independent exponential variables with the same rate parameter follows a gamma distribution. In this case, since each T_i follows an exponential distribution with a rate parameter of 1/100 (mean of 100), the sum ∑_{i=1}^{10} T_i follows a gamma distribution with shape parameter k = 10 and scale parameter θ = 100. Therefore, ∑_{i=1}^{10} T_i ∼ Gamma(10, 100).

(b) To find the probability of successful operation for at least 1.5 years, we need to calculate the cumulative distribution function (CDF) of the gamma distribution at 1.5 years (547.5 days). Using the gamma CDF, denoted by F_X(x), we have:

P(X ≥ 547.5) = 1 - F_X(547.5)

Using the gamma CDF with shape parameter k = 10 and scale parameter θ = 100, we can calculate this probability.

(c) To determine the number of spares needed to be 95% sure of successful operation for at least two years, we need to find the point where the cumulative distribution function (CDF) of the gamma distribution is 0.95. In other words, we need to find the value x such that: P(X ≥ x) = 0.95

Using the gamma CDF with the appropriate shape and scale parameters, we can solve for x.

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Answer:  0

Step-by-step explanation:

Since it is 10 units total from -4 to 6,

4/10 and 6/10 would give a ratio of 2:3

4 units from -4 would be at 0, which is also 6 units away from the 6

4 units to 6 units equals a ratio of 2:3

In this scenario, the probability of selecting each disease is affected by the previous selections, making the study a dependent event.

In order to conduct a Methicillin Resistant Staphylococcus Aureus (MRSA) study, three diseases must be selected from the male ward of a hospital. This ward has 9 cases of osteomyelitis, 7 cases of scaled skin syndrome, and 4 cases of endocarditis. The three diseases will be selected at random, one after the other, without replacement.

It is important to note that MRSA is a bacterium that is resistant to certain antibiotics and is known to cause serious infections in hospitals. Therefore, the study will focus on identifying if MRSA is present in any of the selected diseases. The results of the study will provide important information for the hospital to help prevent and treat MRSA infections.

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Use this:

The basic formula to find the scale factor of a figure is: Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape. This can also be used to calculate the dimensions of the new figure or the original figure by simply substituting the values in the same formula.

Answer:

1 2/3 is the scale factor

Step-by-step explanation:

So the scale factor either makes soemthing bigger or smaller

In this case it’s getting bigger

So we have one side already so we jsut find the value that was multiplied

so 9 * ? Is 15

You

d get 1 2/3

The Graph to the y≥2 and y<4 is attached below.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

The Inequalities are:

y≥2

y<4

Now, if plot these inequalities in the graph we get

The y≥2 will have the shaded on the upper part where y= 2, 3, 4, and so on.

Now,  y < 4 will have the shaded on the lower part of graph where y= 3, 2, 1, 0, -1, -2 and so on.

Now, The shaded region shown the common point between both inequality which is y= 2, 3 4.

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The values of the missing variables from the areas of rectangle and square are;

17) x = 4

18) y = 5

19) x = 4

17) The formula for area of rectangle is;

A = Length * Width

Formula for area of square is;

A = side * side

Thus;

A_rect = (x - 1)(x + 2) = x² + x - 2

A_sq = x²

The area of the rectangle shown exceeds the area of the square by

2 cm². Thus;

x² + x - 2 - x² = 2

x - 2 = 2

x = 4

18) Area of the square; A_sq = y²

Area of the rectangle; A_rect = (y - 3)(y + 1) = y² - 2y - 3

The area of the square exceeds the area of the rectangle by 13 m². Thus;

y² - y² + 2y + 3 = 13

2y = 10

y = 5

19) The area of the square is half the area of the rectangle. Thus;

x² = ¹/₂(2(x² + 2x - 8))

x² = x² + 2x - 8

2x - 8 = 0

x = 4

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Safety data sheets (SDS) are not only required when there are 10 gallons. This statement is false. SDS, also known as material safety data sheets (MSDS), are required for hazardous substances, regardless of the quantity.

Safety data sheets provide detailed information about the potential hazards, handling, and emergency measures for substances. They are required under various regulations, such as the Occupational Safety and Health Administration (OSHA) Hazard Communication Standard (HCS) in the United States.

The quantity of the substance does not determine the need for an SDS. For example, even if a small amount of a highly hazardous substance is present, an SDS is still necessary for safety reasons.

SDS help workers and emergency personnel understand the risks associated with a substance and how to handle it safely. It is essential to follow proper safety protocols and provide SDS for hazardous substances, regardless of the quantity.

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Answer:

X³ – 3x² – 9x – 5

= x³ + x² – 4x² – 4x – 5x – 5

= x²( x + 1) – 4x ( x + 1) – 5(x + 1)

= (x + 1)(x² – 4x – 5)

= (x + 1)(x² -5x + x – 5)

= (x + 1)(x – 5) (x + 1)

hence, (x +1), (x -5) and (x +1) are the factors of given polynomial .

Was this answer helpful?

Answer:

The answer is A

Answer:

Converges by Direct Comparison Test

Step-by-step explanation:

For the infinite series \(\displaystyle \sum^\infty_{n=1}\frac{\sin(9n)}{1+9^n}\), we can use the direct comparison test. We need to check for absolute convergence, so let's assume \(\displaystyle \sum^\infty_{n=1}\biggr|\frac{\sin(9n)}{1+9^n}\biggr|\leq\sum^\infty_{n=1}\frac{1}{1+9^n}\).  Since \(\displaystyle \sum^\infty_{n=1}\frac{1}{9^n}\) is a geometric series with \(\displaystyle r=\frac{1}{9} < 1\), then that series converges. This implies that \(\displaystyle \sum^\infty_{n=1}\frac{1}{1+9^n}\) converges, and so \(\displaystyle \sum^\infty_{n=1}\frac{\sin(9n)}{1+9^n}\) converges by the direct comparison test.

Answer:

6/12

Step-by-step explanation:

all of the other 3 equal 8/12

Answer:

Step-by-step explanation:

The SSA congruence rule states that if two sides and an angle not included between them are respectively equal to two sides and an angle of the other then the two triangles are equal. However, with this congruence rule, two triangles are not said to be congruent since the sides of the two triangles may not be on the same corresponding sides.

Answer:

86.6 feet (3 s.f.)

Step-by-step explanation:

Please see attached picture.

tan60°= height of tower/ 50

Height of tower

= 50tan60°

= 50√3

= 86.6 ft (3 s.f.)

tanѲ= opp/ adj

The probability that Lucy selects a cherry Skittle followed by a lime Skittle is 15/380.

To determine the probability that Lucy selects a cherry Skittle followed by a lime Skittle, we need to consider the total number of Skittles available and the number of cherry and lime Skittles remaining.

Let's calculate the probability step by step:

Step 1: Calculate the probability of selecting a cherry Skittle first.

Lucy has a total of 3 cherry Skittles remaining out of a total of 3 + 5 + 4 + 8 = 20 Skittles remaining.

The probability of selecting a cherry Skittle first is 3/20.

Step 2: Calculate the probability of selecting a lime Skittle second.

After Lucy has eaten the cherry Skittle, she has 2 cherry Skittles remaining, along with 5 lime Skittles out of a total of 19 Skittles remaining.

The probability of selecting a lime Skittle second is 5/19.

Step 3: Calculate the probability of selecting cherry and then lime.

To calculate the probability of two independent events occurring in sequence, we multiply their individual probabilities.

Therefore, the probability of selecting a cherry Skittle first and then a lime Skittle is (3/20) * (5/19) = 15/380.

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Answer: b 4.1%

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

58÷1.095= 53 is the answer

Answer:

5.03196347032

Step-by-step explanation:

We do:

.095x+x=58

1.095x=58

x=52.96

52.96 is a approximation and when you do the math and see what  9.5 of 52.96 plus 52.96 is you get 57.9912 which is super close to 8 The exact answer is x = 5.03196347032

The initial height which the fireworks was launched from the quadratic equation is 2 feet

To determine the initial height at which the fireworks were launched, we need to find the value of h(0), since that represents the height at time t=0 (when the fireworks were launched).

In this giving quadratic equation, all we need to do is put x = 0 to determine the initial height

setting the function to 0

\(h(x) = -x^2 + 10.5x + 2\\h(0) = -(0)^2 + 10.5(0) + 2\\= 2 feet\)

Therefore, the initial height at which the fireworks were launched was 2 feet.

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Arithmetic average return of the company is 2.57%.Geometric average return of the company is 13%.Variance of the company is 56.Standard deviation of the company is 7.48%.

Given, Returns of the company for the last few years are 5%, 10%, -15%, 20%, -12%, 22%, 8%
Arithmetic Average return:
Arithmetic Average return = (sum of all returns) / (total number of returns)
Arithmetic Average return = (5 + 10 - 15 + 20 - 12 + 22 + 8) / 7= 18 / 7= 2.57
Therefore, the arithmetic average return of the company is 2.57%.
Geometric average return:
Geometric average return = [(1+R1) * (1+R2) * (1+R3) * …….. * (1+Rn)]1/n - 1
Geometric average return = [(1.05) * (1.1) * (0.85) * (1.2) * (0.88) * (1.22) * (1.08)]1/7 - 1= 0.13
Therefore, the geometric average return of the company is 13%.
Variance:
Variance = (sum of (return - mean return)2) / (total number of returns)
Mean return = (5 + 10 - 15 + 20 - 12 + 22 + 8) / 7= 18 / 7= 2.57
Variance = [(5-2.57)2 + (10-2.57)2 + (-15-2.57)2 + (20-2.57)2 + (-12-2.57)2 + (22-2.57)2 + (8-2.57)2] / 7= 392.12 / 7= 56
Therefore, the variance of the company is 56.
Standard Deviation:
Standard Deviation = Square root of Variance
Standard Deviation = √56= 7.48
Therefore, the standard deviation of the company is 7.48%.

Thus, Arithmetic average return of the company is 2.57%.Geometric average return of the company is 13%.Variance of the company is 56.Standard deviation of the company is 7.48%.

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To find the value of k in a function, you need to know the equation of the function and the input values for which you want to find the output, and then substitute these values into the equation and solve for k.

A function is a relationship between each element of a non-empty set A and at least one element of another non-empty set B. Functions are the central idea of calculus in mathematics. The functions are special types of relations. A function is a rule that generates a unique outcome for each input x in mathematics.

The collection of all input values that you can use in a function without running into problems or producing undefined results is generally referred to as the domain of the function. When dealing with functions, it is crucial to keep in mind the function's domain because utilizing input values outside of the domain might provide erroneous or undefinable outputs.

To find the value of k in a function, you need to know the equation of the function and the input values for which you want to find the output.

For example, if the function is defined as f(x) = kx + b, and you want to find the value of k for a particular value of x, you can substitute the value of x into the equation and solve for k.

For example, if the function is f(x) = kx + b and you want to find the value of k when x = 2, you can substitute 2 for x in the equation to get:

f(2) = k(2) + b

Solving this equation for k gives:

k = (f(2) - b)/2

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