Please someone help with this!!!!

Let the weight (in kg) of a large box be 'x' and the weight of a small box be 'y'.

Given that the weight of 2 large boxes and 3 small boxes is 78 kg,

Also given that the weight of 6 large boxes and 5 small boxes is 180 kg,

Here we will apply the Elimination Method to solve both the equations.

Consider the three times the first equation being subtracted from the second equation,

Simplify the terms,

Substitute this value in the first equation,

Thus, the larger box weighs 18.75 kg while the small box weighs 13.5 kg

Answer:

14. Reflection

15. A

16. D

Step-by-step explanation:

A reflection creates a mirror image of the original figure because if you think of a mirror, you think of your or an object's reflection.

For number 15, the image is unclear so I will just tell you how to do it. When it says translate 6 units right, and 3 units up, you would need to move every point to the next line, at the right side 6 times. Then, you move every point to the top 3 times and plot your new points.

Number 16 is also unclear, so as many numbers it takes you to get to the x-axis, that is the amount you will move the point away from the exact point on the x-axis. For instance, it takes point C 1 unit to get to the x-axis, so we will plot it 1 point into the x-axis. At the end of this, you should see the image like the pre-image. So it will look like a mirror.

To find the unit vector that points in the same direction as the vector A + 2B, we first calculate the vector A + 2B and then divide it by its magnitude to obtain the unit vector. The unit vector that points in the same direction as A + 2B is (14/15)i^ - (4/9)j^.

The vector A = 12i^ + 14j^ and the vector B = 15i^ - 17j^ are given.

To find the vector A + 2B, we perform the vector addition by adding the corresponding components: A + 2B = (12i^ + 14j^) + 2(15i^ - 17j^).

Simplifying, we get A + 2B = 12i^ + 14j^ + 30i^ - 34j^ = (12 + 30)i^ + (14 - 34)j^ = 42i^ - 20j^.

Next, we calculate the magnitude of the vector A + 2B using the formula: |A + 2B| = √((42)^2 + (-20)^2) = √(1764 + 400) = √2164 ≈ 46.5.

To find the unit vector in the same direction as A + 2B, we divide the vector A + 2B by its magnitude: (42i^ - 20j^) / 46.5.

Dividing each component by 46.5, we get the unit vector: (42/46.5)i^ - (20/46.5)j^.

Simplifying the fractions, we have: (14/15)i^ - (4/9)j^.

Therefore, the unit vector that points in the same direction as A + 2B is (14/15)i^ - (4/9)j^.

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Answer:

  b = 44

Step-by-step explanation:

We can complete the square(s) to put the equation in standard form. Then we can find the value of b that makes the radius be 7 units.

__

  x^2 +y^2 -4x +2y = b . . . . . given

  (x^2 -4x) +(y^2 +2y) = b . . . . group by variable

  (x^2 -4x +4) +(y^2 +2y +1) = b + 4 + 1 . . . . complete the squares

  (x -2)^2 +(y +1)^2 = b +5 = 7^2 = 49 . . . . . write as squares, show radius

  b = 49 -5 = 44 . . . . subtract 5

The value of b to make the radius 7 is 44.

_____

The standard form of the equation for a circle is ...

  (x -h)^2 +(y -k)^2 = r^2 . . . . . center (h, k), radius r

Answer:

The answer is 2.

Step-by-step explanation:

Put the numbers in order, the one that appears most often is the mode.

Answer:

2

Step-by-step explanation:

According to the model, the number of hot drinks that are sold when the temperature is 0 °F is equal to 50 hot drinks.

In Mathematics, the y-intercept is sometimes referred to as a vertical intercept or an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Based on the information provided about the line on the graph (scatter plot), a linear function that models the number of hot drinks that are sold when the temperature is given by:

y = -12x + 50

When x = 0, the number number of hot drinks sold can be calculated as follows;

y = -12(0) + 50

y = 50 hot drinks.

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The answer is y<6

Add 12 to both sides

Simplify

Divide both sides by the same factor

Simplify

For the given expression 2t² is the impulse response, and the given system is linear and the system is unstable

Given, y(t) = 2t{t-4 x(T) dt.
a) To find impulse response, let x(t) = δ(t).Then, y(t) = 2t{t-4 δ(T) dt = 2t.t = 2t².

Let h(t) = y(t) = 2t² is the impulse response.
b) A system is said to be linear if it satisfies the two properties of homogeneity and additivity.

A system is said to be linear if it satisfies the two properties of homogeneity and additivity. For homogeneity,

let α be a scalar and x(t) be an input signal and y(t) be the output signal of the system. Then, we have

h(αx(t)) = αh(x(t)).

For additivity, let x1(t) and x2(t) be input signals and y1(t) and y2(t) be the output signals corresponding to x1(t) and x2(t) respectively.

Then, we have h(x1(t) + x2(t)) = h(x1(t)) + h(x2(t)).

Now, let's consider the given system y(t) = 2t{t-4 x(T) dt.

Substituting x(t) = αx1(t) + βx2(t), we get y(t) = 2t{t-4 (αx1(t) + βx2(t))dt.

By the linearity property, we can write this as y(t) = α[2t{t-4 x1(T) dt}] + β[2t{t-4 x2(T) dt}].

Hence, the given system is linear.
c) A system is stable if every bounded input produces a bounded output.

Let's apply the bounded input to the given system with an input of x(t) = B, where B is a constant.Then, we have

y(t) = 2t{t-4 B dt} = - 2Bt² + 2Bt³.

We can see that the output is unbounded and goes to infinity as t approaches infinity.

Hence, the system is unstable. Therefore, the system is linear and unstable.

Thus, we have found the impulse response of the given system and checked whether the system is linear or not. We have also checked whether the system is stable or unstable. We found that the system is linear and unstable.

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The concept that a message gives different meanings to different objects is called option (b) polymorphism.

Polymorphism is a fundamental concept in object-oriented programming (OOP) that allows different objects to respond to the same message or method invocation in different ways. In other words, it allows objects of different classes to be treated as if they were of the same class, as long as they implement the same method or message.

This can make code more flexible, reusable, and easier to maintain. Polymorphism is achieved through inheritance, interfaces, or overloading methods. For example, a "draw" method could be implemented differently for different shapes, such as circles, rectangles, or triangles.

Therefore, the correct option is (b) polymorphism

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a. Using the calculated z-score, the probability that a randomly chosen bolt has a width between 941 and 957 mm is approximately 0.5558.

b. The appropriate value for C such that a randomly chosen bolt has a width less than C with probability 0.8749 is approximately 963.5 mm.

(a) To find the probability that a randomly chosen bolt has a width between 941 and 957 mm, we can use the z-score formula and the standard normal distribution.

First, let's calculate the z-scores for the given values using the formula:

z = (x - μ) / σ

where:

For x = 941:

z₁ = (941 - 952) / 10 = -1.1

For x = 957:

z₂ = (957 - 952) / 10 = 0.5

Next, we need to find the probabilities corresponding to these z-scores using a standard normal distribution table or a calculator.

Using the standard normal distribution table, we find:

P(z < -1.1) ≈ 0.135

P(z < 0.5) ≈ 0.691

Since we want the probability of the width falling between 941 and 957, we subtract the two probabilities:

P(941 < x < 957) = P(-1.1 < z < 0.5) = P(z < 0.5) - P(z < -1.1) ≈ 0.691 - 0.135 = 0.5558

Therefore, the probability that a randomly chosen bolt has a width between 941 and 957 mm is approximately 0.5558.

(b) To find the appropriate value for C such that a randomly chosen bolt has a width less than C with probability 0.8749, we need to find the z-score corresponding to this probability.

Using a standard normal distribution table or calculator, we find the z-score corresponding to a cumulative probability of 0.8749 is approximately 1.15.

Now, we can use the z-score formula to find the value of C:

z = (x - μ) / σ

Substituting the known values:

1.15 = (C - 952) / 10

Solving for C:

C - 952 = 1.15 * 10

C - 952 = 11.5

C ≈ 963.5

Therefore, the appropriate value for C such that a randomly chosen bolt has a width less than C with probability 0.8749 is approximately 963.5 mm.

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Answer: The formula for rotating 90 degrees clockwise is (y, -x). So your new coordinates is (-3, 2)

Step-by-step explanation:

Answer:

(-3, 2)

Step-by-step explanation:

Answer:

Question 1: Correct

Question 2: Incorrect

Question 3: Correct

Question 4: Correct

Question 7: Correct

Step-by-step explanation:

Question 1: Correct. y = 9 represents a horizontal line, with a zero slope.

Question 2: Incorrect. The given states that the slope is 3. Hence, you're left with two options: either C or D. Substituting (-3, -2) into the given equations:

Option C: y = 3x - 2

-2 = 3(-3) -2

-2 = -9 - 2

-2 = -11 (false statement).  This means that (-3, -2) is not a solution to this equation.

Option D: y = 3x + 7

-2 = 3(-3) + 7

- 2 = -9 + 7

-2 = -2 (True statement). Therefore, Option D is the correct answer for Question 2.

Question 3: Correct. The equation x = 3 represents a vertical line.

Question 4: Correct. The rate of increase is 5,000/2 = 2,500.

Question 7: Correct. The domain is the set of inputs (or x-values) of a given relation. The domain of the given relation is {-2, 0, 3, 4}.

The conclusions that can be made from this table include:

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

From the information, factory A for those who need repairs is 0.05 in the first year. In this case, among cars from factory A, a larger percentage of cars do not need repairs than do need repairs in the first year.

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Answer: C: p - 3g

Step-by-step explanation:

It is correct.

Answer:

3/5 is probability of female out of 5 classmates.

hope it helps

A structural break occurs when we see A. an unexpected shift in time-series data.

It is the change in a time series's data-generating mechanism, it is a phenomenon that occurs when a significant event or structural shift in the economy alters the underlying data-generating mechanism. A structural break can happen for several reasons, including natural catastrophes, changes in economic policy, new inventions, and other reasons that alter the way the data is generated.

In the presence of a structural break, we can't assume that the relationships between variables before and after the break are the same. The primary objective of identifying structural breaks in the time-series is to detect changes in the behavior of the series over time, such as changes in the variance of the series, changes in the mean of the series, and changes in the covariance of the series. So therefore the correct answer is A. an unexpected shift in time-series data, the structural break occurs.

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Dimensions minimizing the cost of constructing the box are -

a = 4.3634  inch , b = 7.6386 inch  , c = 12.0011 inch

Let a be the base if the rectangular box , b to be the height and c to be the  other side of the rectangular box.

Then  the area of the base is = ac

Front box ' s Area  = ab

Area for the remaining other sides =  ab + 2cb

Cost of the base of the box = 7ac

Cost of the front of the box = 9ab

The remainder of the sides will cost = 2(ab + 2cb)

So, the total cost  C is

C = 7 ac + 9 ab + 2(ab + 2cb)

C = 7 ac + 9 ab + 2ab + 4cb

C = 7 ac + 11 ab + 4cb   ---- (1)

Rectangular box's volume is given by ,

⇒V = abc = 400 in³

If abc = 400

Then b = 400/ac

Replacing the value of  c in the above equation -

C = 7ac + 4400/c + 1600/a

On differentiating C with respect to a and c; we have -

Cᶜ = 7a - 4400/c² .....[2] [ respect to c ]

Cᵃ = 7c - 1600/a² .....[3] [ respect to a ]

Now, on equating equations 2 and 3 to zero.

a = 4400/7c² ....[4]

c = 1600/7 a² .....[5]

Now ,  from equations 4 and 5

c = 1600 / 7 [4400/7c²]²

On solving the above equation -

c = 12.0011

Putting the value of c in [5]

a = 4.3634

b's value can be determined by  -

b = 400/4.3634 * 12.0011

b = 7.6386

Thus,  dimensions resulting to minimize the cost of constructing the box is:

a = 4.3634  inch , b = 7.6386 inch  , c = 12.0011 inch

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Answer:

The length = 5x + 25

Step-by-step explanation:

A = l x w

Answer:

I have something you might like!

Here's the key ;)

Step-by-step explanation:

I would appreciate Brainliest! I hope I helped! :)

Step-by-step explanation:

3972/41 the answer of this is

=96.87

No, the variances are not similar enough to use the pooled t test. The ratio of the two variances (25/8) is greater than 3, which is the typical cutoff for determining similarity of variances. Therefore, an alternative method such as the Welch's t-test or a non-parametric test should be used to compare the means.

To determine if the variances are similar enough to use a pooled t-test, you can perform an F-test for equality of variances. Follow these steps:

1. Calculate the F statistic by dividing the larger variance by the smaller variance: F = var2 / var1 = 25 / 8 = 3.125.

2. Determine the degrees of freedom for each group: df1 = 10 - 1 = 9 and df2 = 10 - 1 = 9.

3. Check the F critical value for the given degrees of freedom and chosen significance level (e.g., 0.05) using an F-distribution table or a calculator. For df1 = 9 and df2 = 9 at a 0.05 significance level, the F critical value is approximately 3.18.

4. Compare the calculated F statistic to the F critical value: 3.125 < 3.18.

Since the F statistic is less than the F critical value, we fail to reject the null hypothesis that the variances are equal. Therefore, the variances are similar enough to use the pooled t-test to evaluate differences in the means. The answer is yes.

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Answer:

16u^2 and 16u

Step-by-step explanation:

Hello! :)

Well, the only difference in the two points is from the 0 and the -4. That means the square is 4 units in length and width.

A=B*H=4*4=16 u^2

P=B*4=4*4=16 u

Answer:

5

Step-by-step explanation:

The mean is 6 and there are 5 intergers.

You'd multiply 5*6=30. That means that the sum is 30.

The values could be: 2 3 7 9 9

These values add up to 20

Have a mode of 9

Have a median of 7

Have a mean of 6

To find the range you would subtract 9 and 2. That gives you 5.

(i don't know if that's the greatest possible range. But 5 would be the range here)

To find the probability that the amount of pollutant in a given sample will exceed 1/2 for the smokestack with the filter installed, you need to determine the distribution of the pollutant levels and then calculate the probability based on that distribution.

To find the probability that the amount of pollutant in a given sample will exceed 1/2 when a filter is installed in the smokestack, we need to use the information provided in the question. However, we do not have any specific information on the distribution of the pollutant levels, so we cannot calculate the exact probability.
Instead, we can make some assumptions based on the purpose of the filter. Filters are typically installed to reduce the amount of pollutants emitted into the air, so it is reasonable to assume that the filter will decrease the amount of pollutant in each sample. Therefore, we can expect the probability of the pollutant level exceeding 1/2 to decrease when a filter is installed.
Without more information, we cannot give an exact probability, but we can say that it is likely lower than the probability without a filter. We would need to know more about the specific characteristics of the filter and the pollutant to make a more accurate estimate.

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Answer:

Step-by-step explanation:

\(2x - 14 = 3x + 6\)

Move 3x to the other side of the equation

\(2x - 3x - 14 = 6 \\ - x - 14 = 6\)

Move -14 to the right side of the equation.

\( - x = 14 + 6 \\ - x = 20\)

Multiply both sides by - 1

\( - ( - x) = - 20 \\ x = - 20\)

We have the final answer as

Hope this helps you

Answer: add 14 to both sides of the equation

2x-14=3x+6

2x-14+14=3x+6+14

Simplify

add the numbers

2x-14+14=3x+6+14

2x=3x+6+14

add the numbers

2x=3x+6+14

2x=3x+20

subtract 3x from both sides of the equation

2x=3x+20

2x-3x=3x+20-3x

simplify

Combine like terms

2x-3x=3x+20-3x

-x=3x+20-3x

Combine like terms

-x=3x+20-3x

-x=20

Divided both sides of the equation by the same term

-x=20

-x/-1=20-/-1

Simplify

Cancel terms that are in both the numerator and denominator

-x/-1=20/-1

x=20/-1

Divide the numbers

x=20/-1

x=-20

So the answer is x=-20

Hope this helps... Stay safe and have a great day/night!!! :D

Answer:

$6

Step-by-step explanation:

you will save 6 dollars per item

Answer:

(0) = 0.9(-6.333) - 5.7

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The problem with D is that 7 + 11 = 18. The rule is any two sides must exceed the third. D gives the shorter + the middle length = the longest length.

That can't work. All the others are fine.

Answer:

A(-3,4)

Step-by-step explanation:

The solution of the inequality y < 2x + 3 will be;

⇒ (3, 0)

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ y < 2x + 3

Now,

Since, The inequality is,

⇒ y < 2x + 3

Hence, The solution of the inequality is,

For point (- 3,4);

⇒ y < 2x + 3

⇒ 4 < 2 × - 3 + 3

⇒ 4 < - 3

Which is not true.

For point (3,0);

⇒ 0 < 2x + 3

⇒ 0 < 2 × 3 + 3

⇒ 0 < 9

Which is true.

Thus, The solution of the inequality y < 2x + 3 will be;

⇒ (3, 0)

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If you add a small imperfection to a system that has saddle-node bifurcation, the system will experience a phenomenon known as "imperfect bifurcation."

This means that the bifurcation will not occur at a single, well-defined point, but rather over a range of parameter values. This can lead to a change in the dynamics of the system, such as the appearance of new attractors or the disappearance of existing ones. In general, imperfect bifurcation can make the behavior of a system more complex and difficult to predict.

Moreover, the specific effect of the imperfection will depend on its size, location, and nature, and can vary between different types of saddle-node bifurcations, such as fold or transcritical bifurcations. Therefore, the analysis of imperfect bifurcation requires a detailed understanding of the system's dynamics and the effects of perturbations.

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