Fernando works in the shipping department of a toy manufacturer. Toy cars weigh 3
kilograms apiece and are shipped in a container that weighs 5 kilograms when empty. Toy
trucks, which weigh 2 kilograms apiece, are shipped in a container weighing 10 kilograms.
When packed with toys and ready for shipment, both kinds of containers have the same
number of toys and the same weight. What is the weight of each container?
Write a system of equations, graph them, and type the solution.

Answer: Choice D)  7.5 inches, 18 inches, 19.5 inches

====================================================

Explanation:

The Pythagorean theorem converse can be used to determine if we have a right triangle or not.

The converse says that if a^2 + b^2 = c^2 is a true equation, then we have a right triangle.

The value of c is always the longest side. The order of 'a' and b doesn't matter (usually b is larger than or equal to 'a'). So we could have \(a \le b < c\) or \(b \le a < c\), but convention usually leans toward the first inequality mentioned.

----------------------------------

In choice A, we have the following steps

a^2 + b^2 = c^2

(7.5)^2 + (18)^2 = (21.5)^2

380.25 = 462.25

Since the third equation is false, this means the first equation is false for those a,b,c values. Choice A is not a right triangle. We can cross it off the list.

----------------------------------

In choice B, we have a = 7.5, b = 19.5 and c = 21.5

So,

a^2 + b^2 = c^2

(7.5)^2 + (19.5)^2 = (21.5)^2

436.5 = 462.25

which is also false. Cross choice B off the list.

-----------------------------------

With choice C we have: a = 18, b = 19.5, c = 21.5

a^2 + b^2 = c^2

(18)^2 + (19.5)^2 = (21.5)^2

704.25 = 462.25

Cross choice C off the list since the third equation is false.

-------------------------------------

In choice D, we have the sides a = 7.5, b = 18, c = 19.5

a^2 + b^2 = c^2

(7.5)^2 + (18)^2 = (19.5)^2

380.25 = 380.25

We get the same number on both sides, so the third equation is true. Consequently, this leads to the first equation being true for those a,b,c values. Choice D is a right triangle, and it's the final answer.

This, compute f30  = (832040, 1346269)t.

To solve the given problem in MATLAB

Define the matrix f.

f = [0 1; 1 1];

Find the eigenvalues and eigenvectors of matrix f.

[V, D] = eig(f);

Obtain the invertible matrix p and the diagonal matrix d.

p = V;

d = D;

Verify that pdp^(-1) equals f.

result = p * d * inv(p);

Compute f^10 and pd^10p^(-1).

f_10 = f^10;

result_10 = p * (d^10) * inv(p);

Compute ff, f2f, f3f, f4f, and f5f.

f_1 = f * f;

f_2 = f_1 * f;

f_3 = f_2 * f;

f_4 = f_3 * f;

f_5 = f_4 * f;

The pattern in the answers can be observed as follows:

ff = (1, 1)t

f2f = (1, 2)t

f3f = (2, 3)t

f4f = (3, 5)t

f5f = (5, 8)t

To compute f30, we can use the same pattern and repeatedly multiply f with itself. However, computing f^30 directly might result in large numbers and numerical errors. Instead, we can utilize the Fibonacci sequence properties.

Given that f = (f0, f1)t = (1, 1)t, we know that fnf = (fn, fn+1)t. So, to find f30, we can calculate f30f = (f30, f31)t. Since f30 is the 31st term in the Fibonacci sequence, we can conclude that f30 = fn+1 = 832040.

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Dialogue can be used today to foster understanding and reconciliation between Indigenous and non-Indigenous Canadians by providing a platform for sharing perspectives, addressing historical truths, and promoting empathy and mutual respect.

Dialogue plays a crucial role in facilitating communication and understanding between different groups. In the context of Indigenous and non-Indigenous Canadians, dialogue can help bridge the gap between their beliefs and histories. By engaging in open and respectful conversations, both groups can share their perspectives, beliefs, and experiences, leading to a deeper understanding of each other's truths.

Dialogue provides an opportunity to address historical truths and the impacts of colonization and assimilation policies on Indigenous communities. Through dialogue, non-Indigenous Canadians can gain a better understanding of the injustices and systemic issues faced by Indigenous peoples. It allows for the acknowledgement of past wrongs, promoting healing and reconciliation. Furthermore, dialogue encourages the development of empathy and mutual respect. By actively listening and engaging in dialogue, both Indigenous and non-Indigenous Canadians can develop a greater appreciation for each other's beliefs, values, and cultural heritage. It creates space for building connections, fostering trust, and working towards a more inclusive and equitable society.

Dialogue serves as a powerful tool to facilitate understanding, truth-telling, and reconciliation between Indigenous and non-Indigenous Canadians. It allows for the sharing of perspectives, addressing historical truths, and promoting empathy and mutual respect. Through dialogue, both groups can move forward in building stronger relationships and working towards a more just and inclusive society.

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Answer:

See below!

Step-by-step explanation:

1) 720cm - m

2) 983 mm - m

3) 130.5kL - L

4) 0.03 g - mg

5) 997 g - kg

6) 9.1 l - ml

7)3.75 c - ml

8) 41.8 in - cm

9) 156.25 lb - kg

10) 9.5 gal - l

11) 680.4 g - lb

12) 4.725 m - ft

Hope this helps, have a lovely day! :)

Answer:

x=62

Step-by-step explanation:

a triangle equals 180

so knowing that you subtract 56 from 180

That gives you 124

Then you divide it by 2 because the sides are equal.

That gives you 62

so x=62

Answer:

2d

Step-by-step explanation:

The n th term of an AP is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference, thus

a₃ - a₁

= a₁ + 2d - a₁

= 2d

(a)An function the deformation gradient F is F = 1 γ 0,0 2X2 0,0 0 1

(b The right Cauchy-Green deformation tensor C is C = 1+γ²γ 0,

γ 4X2²0,0 0 1 the left Cauchy-Green deformation tensor B is B = 1+γ² γ 0,γ γ²+4X2² 0,0 0 1.

(a) Deformation Gradient F:

The deformation gradient is defined as the derivative of the deformed coordinates x with respect to the initial coordinates X:

F = ∂x/∂X

Given the shear deformation x = φ(X) with x1 = X1 + γX2, x2 = X2X2, and x3 = X3, we can compute the deformation gradient as follows:

F =∂x1/∂X1 ∂x1/∂X2 ∂x1/∂X3

∂x2/∂X1 ∂x2/∂X2 ∂x2/∂X3

∂x3/∂X1 ∂x3/∂X2 ∂x3/∂X3

Taking the partial derivatives:

∂x1/∂X1 = 1, ∂x1/∂X2 = γ, ∂x1/∂X3 = 0

∂x2/∂X1 = 0, ∂x2/∂X2 = 2X2, ∂x2/∂X3 = 0

∂x3/∂X1 = 0, ∂x3/∂X2 = 0, ∂x3/∂X3 = 1

(b) Right and Left Cauchy-Green Deformation Tensors C and B:

The right Cauchy-Green deformation tensor C is defined as the square of the deformation gradient:

C = F²T × F

The left Cauchy-Green deformation tensor B is defined as the square of the transpose of the deformation gradient:

B = F × F²T

Calculating C:

C = F²T × F

C = 1 0 0

γ 2X2 0

0 0 1

1 γ 0

0 2X2 0

0 0 1

C =1+γ² γ 0

γ 4X2² 0

0 0 1

Calculating B:

B = F × F²T

B = 1 γ 0

0 2X2 0

0 0 1

1 0 0

γ 2X2 0

0 0 1

B = 1+γ² γ 0

γ γ²+4X2² 0

0 0 1

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There were no suspects with less than two prior arrests in this scenario.

Let's solve the problem step by step:

Let's assume the number of suspects with one prior arrest is "x" and the number of suspects with two prior arrests is "y".

According to the given information:

The total number of suspects is 6.

So, x + y = 6 -- (Equation 1)

The total number of arrests, including yesterday's arrests, is 16.

The number of arrests for suspects with one prior arrest is x + 1 (yesterday's arrest plus their one prior arrest).

The number of arrests for suspects with two prior arrests is 2y (yesterday's arrest plus their two prior arrests).

So, (x + 1) + 2y = 16 -- (Equation 2)

Now, we have a system of two equations (Equation 1 and Equation 2) that we can solve to find the values of x and y.

Solving the equations:

From Equation 1, we can rewrite it as x = 6 - y and substitute it into Equation 2:

(6 - y + 1) + 2y = 16

7 - y + 2y = 16

y + 7 = 16

y = 16 - 7

y = 9

Now, substitute the value of y back into Equation 1 to find x:

x = 6 - y

x = 6 - 9

x = -3

Since we cannot have a negative number of suspects, we conclude that there was an error in the given information or calculations.

Therefore, there were no suspects with less than two prior arrests in this scenario.

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Answer:

x=10

Step-by-step explanation:

15+2x=5+3x

15=5+x

10=x

When measuring wind speed with a cup anemometer on a sailboat trip across the Atlantic Ocean, there are a few situations that may arise, as shown below:1. When the bearing of the axle is old, the type of error that occurs is systematic error. To reduce or overcome this error, you would need to replace the bearing to avoid it.

2. When there is turbulent flow, the type of error that occurs is random error. To overcome this error, you would have to wait for the wind to stabilize or take an average of many measurements.  3. When there is icing on the cups, the type of error that occurs is also random error.

To overcome this error, you would need to remove the ice or wait for it to melt before continuing the measurement.4. When there is strong tumbling of the sailboat, the type of error that occurs is systematic error. To overcome this error, you would need to find a way to stabilize the boat or take measurements when the boat is less unstable.

It is not well posed to use a cup anemometer to measure in-cabin air flow in a quiet environment because the device is not sensitive enough. The device needs a minimum wind speed to provide accurate readings, and it is not designed to measure low wind speeds. Therefore, it may not be the right tool for the job, and a different instrument may be more appropriate.

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Given :

Miki has 104 nickels and 88 dimes. She wants to divide her coins into groups where each group has the same number of nickels and the same number of dimes.

There were 216,000 cars sold last year.

To Find :

Equation that can be used to find the number of trucks, t, sold last year.

Solution :

Let , number of truck sold is t and number of car sold is c.

It is given that the number of cars sold was 39,000 more than three times the number of trucks sold.

So ,

\(c=3t+39000\\\\t=\dfrac{c-39000}{3}\)

Putting value of c = 216000 in above equation , we get :

\(t=\dfrac{c-39000}{3}\\\\t=\dfrac{216000-39000}{3}\\\\t=59000\)

Hence , this is the required solution .

​

An equation is formed of two equal expressions. An equation that can be used to find the number of trucks, t is 216,000 = 39,000 + 3t.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that in the Last year, the number of cars sold was 39,000 more than three times the number of trucks sold. Therefore, we can write,

Number of cars sold = 39,000 + 3 times the number of trucks sold

Number of cars sold = 39,000 + 3t

where t represents the number of trucks sold.

Given that number of cars sold is 216,000. Therefore, the equation can be solved for t as shown below.

216,000 = 39,000 + 3t

216,000 - 39,000 = 3t

3t = 177,000

t = 177,000 / 3

t = 59,000

Hence, an equation that can be used to find the number of trucks, t is 216,000 = 39,000 + 3t.

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Answer:

its 1,b 2,c 3,a

so letter C

Step-by-step explanation:

Have a wonderful day!

The probability that at most one of their seven children will have that trait is 0.0188416

From the question, the given parameters are

Number of children, n = 7

Probability of a child with the trait, p = 60%

The required probability that at most one will have that trait is represented as P(x ≤ 1)

This probability is calculated using

P(x ≤ 1) = P(0) + P(1)

Where

P(x) = ⁿCₓ * pˣ * (1 - p)ⁿ⁻ˣ

So, we have

P(x ≤ 1) = ⁷C₀ * (60%)⁰ * (1 - 60%)⁷⁻⁰ + ⁷C₁ * (60%)¹ * (1 - 60%)⁷⁻¹

Evaluate

P(x ≤ 1) = ⁷C₀ * 1 * (40%)⁷ + ⁷C₁ * (60%) * (40%)⁶

So, we have

P(x ≤ 1) = 0.0188416

Hence, the probability is 0.0188416

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Answer:

It is D

Step-by-step explanation:

The equation of the horizontal asymptote is  y = − 4  .Horizontal Asymptote:  y = - 4

The shortest distance Hannah will have to run to see both a drink station and direction marker at the same location is 3500 meters.

The least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.

Given:

She will be running while her other team members swim and bike.

Hannah will see a direction marker every five hundred meters during the race.

There will be drinks stations set up every seven hundred meters.

The shortest distance Hannah will have to run to see both a drink station and direction marker at the same location is,

= LCM of 500 and 700

= 3500 meters.

Therefore, the distance is 3500 meters.

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From the situation described, we have that:

a) The combinations are: {{A1,S1}, {A1,S2}, {A1,S3}, {A2,S1}, {A2,S2}, {A2,S3}, {A3,S1}, {A3,S2}, {A3,S3}, {A4,S1}, {A4,S2}, {A4,S3}}.

b) All the combinations were listed listing each of the art activities with each possible sport activity.

c) Using the Fundamental Counting Theorem, there are 12 combinations.

It is a theorem that states that if there are n things, each with \(n_1, n_2, \cdots, n_n\) ways to be done, each thing independent of the other, the number of ways they can be done is:

\(N = n_1 \times n_2 \times \cdots \times n_n\)

Considering that there are 4 art activities and 3 sport activities, the parameters are given as follows:

\(n_1 = 4, n_2 = 3\)

Hence the number of combinations is:

N = 4 x 3 = 12.

Then:

a) The combinations are: {{A1,S1}, {A1,S2}, {A1,S3}, {A2,S1}, {A2,S2}, {A2,S3}, {A3,S1}, {A3,S2}, {A3,S3}, {A4,S1}, {A4,S2}, {A4,S3}}.

b) All the combinations were listed listing each of the art activities with each possible sport activity.

c) Using the Fundamental Counting Theorem, there are 12 combinations.

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A triangle with two congruent sides(if they have the same shape and size) is not always a 45-45-90 triangle. So the given statement is false.

A 45-45-90 triangle is a special type of right triangle where the two legs (the sides adjacent to the right angle) are congruent, and the hypotenuse (the side opposite the right angle) is the square root of 2 times the length of the legs.

However, there are other triangles with two congruent sides that are not 45-45-90 triangles. For example, an isosceles triangle has two congruent sides but does not necessarily have a 45-degree angle. The angles of an isosceles triangle can vary depending on the specific lengths of the sides.

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Answer:

They will have the same amount of CDs on the third month

they will both have 33

Step-by-step explanation:

These steps are often referred to as the principle of mathematical induction or PMI.

The steps for mathematical induction are:

Base Case: Show that the statement holds for some particular value of n, usually n = 1 or n = 0.

Inductive Hypothesis: Assume that the statement holds for some arbitrary value of n = k, where k is a positive integer.

Inductive Step: Using the inductive hypothesis, show that the statement also holds for n = k + 1.

Conclusion: By the principle of mathematical induction, the statement is true for all positive integers n.

These steps are often referred to as the principle of mathematical induction or PMI. They are used to prove statements that involve an infinite set of integers by showing that the statement holds for a base case, assuming that it holds for an arbitrary value, and then showing that it holds for the next integer in the set.

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Answer:  (-6,7)

Step-by-step explanation:

Tow points, (x1, y1) and (x2, y2) are simetric in a quadratic graph when:

f(x1) = y1 = f(x2) = y2

so y1 = y2

Then if we have the point (2,7) we want to find other point that has the same value for y, this is (-6, 7)

So the correct option is  (-6,7)

Answer:

C. 5:12

Explanation:

Answer:

I think its wrong. For g(5)=(5/5)^2=1 and in your graph is something close to 3. The correct graph for \(g(x)=(\frac{1}{5}x)^2\) is

Answer:

False

Step-by-step explanation:

Took the test and this is what I got

Answer:

Sample space = { 1, 2, 3, 4, 5, 6}

Explanation:

The sample space is the set with all the possible outcomes of the experiment. So if we roll a 6 sided die, we have the possible outcomes:

{ 1, 2, 3, 4, 5, 6}

Because we have 6 possible results. one for every side of the die

Therefore, the sample space is { 1, 2, 3, 4, 5, 6}

Answer:

42

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

hope this helps!

Answer: Rs. 360

Step-by-step explanation:

let x of 12 1/2%=45

=> x.25/200=45

=> x/8=45

=> x=45.8

=> x=360

it is Rs 360

Answer:

6 units to the right

Step-by-step explanation:

Hope this helps!

The correct option is that in science, a theory encompasses many hypotheses.

In science, a theory is a well-established explanation that is supported by scientific evidence and is extensively tested through experimentation and observation.

It's a big idea that includes several connected hypothese that have been thoroughly investigated and found to be true. A theory that hasn't been put to the test is called a hypothesis.

A hypothesis is a proposed explanation that is subject to further testing. It's an untested hypothesis that hasn't yet undergone experimental validation. Theories are the result of a drawn-out and labor-intensive process of experimentation and observation.

They can never be established as an absolute answer to a scientific problem. Instead, they lay the groundwork for additional investigation and experimentation in that field of study.

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the gamma distribution becomes approximately normal due to the Central Limit Theorem when n is large.X ︽.Norm(a/λ, a/λ²) since it is an approximately normal distribution with mean a/λ and variance a/λ².

(a) Gamma random variables are sums of random variables, and as n gets large, the Central Limit Theorem applies. When n is large, the gamma random variable with parameters (n, λ) approaches a normal distribution, as the sum of independent and identically distributed Exponential(λ) random variables is distributed roughly as a normal distribution with mean n/λ and variance n/λ². In other words, the gamma distribution becomes approximately normal due to the Central Limit Theorem when n is large.

(b) The problem asks to show that:lim (1 + x/n)-n = e⁻x.The expression (1 + x/n)⁻ⁿ can be written as [(1 + x/n)¹/n]ⁿ. Now letting n → ∞ in this equation and replacing x with aλ yields the desired result from part (a):lim (1 + x/n)ⁿ

= lim [(1 + aλ/n)¹/n]ⁿ

= e⁻aλ(d)

The central limit theorem with continuity correction can be expressed as:P(Z ≤ z) ≈ Φ(z + 0.5/n)if X ~ B(n,p), where Φ is the standard normal distribution and Z is the standard normal variable.

This continuity correction adjusts for the error made by approximating a discrete distribution with a continuous one.(e) The exact probability that the walk is within 500 steps from the origin can be calculated by using the normal distribution. Specifically, we have that:

P(|X - a/λ| < 500)

= P(-500 < X - a/λ < 500)

= P(-500 + a/λ < X < 500 + a/λ)

= Φ((500 + a/λ - μ)/(σ/√n)) - Φ((-500 + a/λ - μ)/(σ/√n)),

where X ~ N(μ, σ²), and in this case, μ = a/λ and σ² = a/λ².

Therefore, X ︽.Norm(a/λ, a/λ²) since it is an approximately normal distribution with mean a/λ and variance a/λ².

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