Can someone help me out with these math questions?
You can pick one to answer or chose to answer both!
I’d appreciate the help thank you!

Answer:

(3,-1) is a solution but (4,3) is not a solution

Step-by-step explanation:

You simply look to see if x in both ordered pairs are 3 since you are given the equation x=3 then x needs to equal 3 for it to be valid

Answer:

D Medicine developed from strands of bacteria is an example of how microorganisms can be helpful.

Seeing that both triangles are side by side and share a side, we know that that side of both triangles is congruent.

Then when you look at the angles, you will see that one on each triangle has one curved line. This one curved line shows that these angles are congruent.

There is then the two curved lines you can find on both triangles as well. This shows that both those angles are congruent.

With this information, you should be able to tell that two angles of the triangles are congruent, and one side of both triangles are congruent, with the order that these are shown on the triangles being an angle, then a side, then another angle, the answer would be ASA, or angle, side angle.

Answer:

here you go , all four completed, took me some time , hipe i was able to help you out tho

After using the test statistic z, P(3.6<X<53.5) = 0.967.

In the given question, suppose X is a normal random variable with mean 35 and sdev 10.

We have to find P(3.6<X<53.5).

Fro the given question,

Mean x = 35

sdev s = 10

Z = X - mu / sd

P(3.6<X<53.5) = P ( 3.6-35/10 < Z < 53.5-35/10 )

P(3.6<X<53.5) = P ( -31.4/10 < Z < 18.5/10 )

P(3.6<X<53.5) = P ( -3.14 < Z < 1.85 )

P(3.6<X<53.5) = P ( Z < 1.85) - P ( Z < -3.14)

left tail of both

P(3.6<X<53.5) = 0.9678 - 0.0008

P(3.6<X<53.5) = 0.967

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The right answer is:

Suppose X is a normal random variable with mean 35 and sdev 10. Find P(3.6<X<53.5)

Answer:

Hello. y=1/2x-2

Step-by-step explanation:

The line that is perpendicular to this line ،its slope must be 1/2

So:

\(y - y0 = m(x - x0) \\ y - 2 = \frac{1}{2} (x - 8) \\ y = \frac{1}{2} x - 2\)

Answer:

58.3 repeated

Step-by-step explanation:

hope this helps :)

The solutions are,

The radians wade sweep out is 2.875 radians.

When wade stops skiing, he is 0.799km to the right of the center of the ski trail.

When wade stops skiing, he is 0.003km above the center of the ski trail.

Given that;

Wade is traveling along a 0.8 km-radius circular ski trail. Wade moves 2.3 kilometers counterclockwise starting at the three o'clock position.

Radius (r) = 0.8km

Distance (s) = 2.3km

Here, we need to find three cases, they are;

Case(I): how many radians does wade sweep out;

The relation between radians and radius is given by,

s = rθ

2.3 = 0.8*θ

θ = 2.3/0.8

θ = 2.875

The radians wade sweep out is 2.875 radians.

Case (II): when wade stops skiing, how many km is wade to the right of the center of the ski trail;

Let, Ф = π - 2.875

      Ф = 0.266 radians

Then, x = r*cosФ

          x = 0.8*cos(0.266)

          x = 0.799

When wade stops skiing, he is 0.799km to the right of the center of the ski trail.

Case (III): when wade stops skiing, how many km is wade above the center of the ski trail;

Let, y = r*sinФ

      y = 0.8*sin(0.266)

      y = 0.003

When wade stops skiing, he is 0.003km above the center of the ski trail.

Therefore, the required solutions are;

The radians wade sweep out is 2.875 radians.

When wade stops skiing, he is 0.799km to the right of the center of the ski trail.

When wade stops skiing, he is 0.003km above the center of the ski trail.

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The simplified expression for the given expression is "a squared minus b squared minus a b."

To simplify the given expression, let's break it down step by step:

- Negative 2 a squared b a squared: This term remains the same in the simplified expression.

- Minus 5 a b: This term remains the same in the simplified expression.

- 3 a b squared minus b squared: This can be simplified as (3 a b squared) - (b squared) = 3 a b squared - b squared.

- 2 (a squared b 2 a b): This can be simplified as 2 (a squared b) - 2 (a b) = 2 a squared b - 2 a b.

Now, combining all the simplified terms, we have:

-2 a squared b a squared - 5 a b + 3 a b squared - b squared + 2 a squared b - 2 a b

Simplifying further, we can group like terms:

-2 a squared b + 2 a squared b - 5 a b - 2 a b + 3 a b squared - b squared

Combining like terms, we get:

0 - 7 a b + 3 a b squared - b squared

Finally, rearranging the terms in decreasing order of degree, we have:

- b squared + 3 a b squared - 7 a b

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The least amount of time spent per week on meetings for the sample of 25 CEOs is 12 hours.

The least amount of time spent per week on meetings for the sample of 25 CEOs can be found by looking at the lowest value in the data set. The data set provided above lists the time spent per week on meetings for a sample of 25 CEOs, and the least amount of time spent is 12 hours per week.

This is the smallest value in the data set, and it represents the minimum amount of time spent on meetings among the CEOs in the sample.

Note that this data is a sample of 25 CEOs and not the entire population of CEOs, so it is not representative of all CEOs. Additionally, the time spent per week on meetings is a quantitative variable, and it is continuous. Therefore, it is recommended to use measures of central tendency (mean or median) and measures of dispersion (standard deviation, range) to make inferences about the population.

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The proof by mathematical induction shows that the statement 1^3 + 2^3 + 3^3 + n^3 = (n^2(n+1)^2)/4 holds for all positive integers n. The base case n = 1 is true, and assuming the statement is true for n = k, we can prove it is true for n = k+1 by substituting k+1 for n and simplifying the expression.

To prove the statement 1^3 + 2^3 + 3^3 + ... + n^3 = (n^2(n+1)^2)/4 for all natural numbers n using mathematical induction, we proceed as follows:

Base case: Let n = 1. Then 1^3 = (1^2(1+1)^2)/4 = 1, which is true.

Inductive step: Assume the statement is true for some arbitrary value k, i.e., 1^3 + 2^3 + 3^3 + ... + k^3 = (k^2(k+1)^2)/4.

We need to show that the statement is also true for n = k+1, i.e., 1^3 + 2^3 + 3^3 + ... + (k+1)^3 = ((k+1)^2(k+2)^2)/4.

Starting with the left-hand side of the equation, we have:

1^3 + 2^3 + 3^3 + ... + (k+1)^3

= (1^3 + 2^3 + 3^3 + ... + k^3) + (k+1)^3 // regrouping the last term

= (k^2(k+1)^2)/4 + (k+1)^3 // using the induction hypothesis

= (k+1)^2(k^2+4k+4)/4 // factoring out (k+1)^2

= ((k+1)^2(k+2)^2)/4 // simplifying the expression

Therefore, the statement is true for n = k+1, and by mathematical induction, the statement is true for all natural numbers n.

Hence, we have proven that 1^3 + 2^3 + 3^3 + ... + n^3 = (n^2(n+1)^2)/4 for all natural numbers n.

Your question is incomplete.

Complete question may be:

Use mathematical induction to prove that statement 1^3 + 2^3 + 3^3 + n^3 = (n^2(n+1)^2)/4 , ∀n∈N

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(a) By plugging in different values for x1, we can plot the indifference curves passing through the given points (2, 2), (1, 2), and (4, 2).

(b) The shape of the indifference curves shows convexity.

(c) The property used to determine this is the non-satiation property of preferences.

(d) The Walrasian demand may not always be single-valued.

(e) Receiving the voucher makes the consumer better-off .

(f) The cash payment allows the consumer to maximize utility by making trade-offs

For 4x1 + x2 = x1 + 2x2, rearranging the equation gives x2 = 3x1, representing the linear part of the indifference curves.

For x1 + 2x2 = 4x1 + x2, rearranging the equation gives x2 = 3x1, representing the kink in the indifference curves.

By substituting different values for x1, we can plot the indifference curves. They will be upward sloping straight lines with a kink at x2 = 3x1.

(b) Properties of the preferences deduced from the shape of indifference curves and utility function:

Diminishing Marginal Rate of Substitution (MRS): Indifference curves are convex, indicating diminishing MRS. The consumer is willing to give up less of one good as they consume more of it, holding the other good constant.

Non-Satiation: Indifference curves slope upwards, showing that the consumer prefers more of both goods. They always prefer bundles with higher quantities.

Convex Preferences: The kink in the indifference curves indicates convexity, implying risk aversion. The consumer is willing to trade goods at different rates depending on the initial allocation.

(c) UMP does not have a solution when Pk = 0 and X -> R2+. This violates the assumption of finite resources and prices required for utility maximization. The property used is non-satiation, as a consumer will always choose an infinite quantity of goods when they are available at zero price.

(d) Walrasian demand depends on relative prices:

If p1 = p2 > 4, the maximizing bundle lies on the linear portion of indifference curves, where x2 = 3x1.

If 4 < p1 = p2 < 1/2, the maximizing bundle lies on the linear portion of indifference curves but at lower x1 and x2.

If p1 = p2 < 1/2, the maximizing bundle lies at the kink point where x1 = x2.

Walrasian demand may not be single-valued due to the shape of indifference curves and the kink point, allowing for multiple optimal solutions based on relative prices.

(e) Given p1 = p2 = 1 and w = $60, the initial budget set is x1 + x2 = 60. With a $10 voucher for good 1, the new budget set becomes x1 + x2 = 70. Since p1 = 1, the consumer spends the voucher on good 1, resulting in x1 = 20 and x2 = 40. Receiving the voucher improves the consumer's welfare by allowing more consumption of good 1 without reducing good 2.

(f) If given the choice between a $10 cash payment and a $10 voucher for good 1 only, the consumer would choose the cash payment. It provides flexibility to allocate the funds based on individual preferences. The answer remains the same even if the assistance were $30, as the cash payment still allows optimal allocation based on preferences. Cash payment offers greater utility-maximizing options compared to the voucher, which restricts choices.

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Answer: 3

Step-by-step explanation:

The amount of work required to empty the trough by pumping the water over the top is 434 foot-pounds.

To find the amount of work required to empty the trough by pumping the water over the top, we need to calculate the volume of water in the trough and then multiply it by the weight of water to determine the work.

First, let's determine the equation of the graph y = 1, which represents the shape of the cross-section of the trough parallel to one end. Since it's a horizontal line at y = 1, the equation is simply y = 1.

Next, let's find the length of the trough. Given that x ranges from -1 to 6, the length of the trough is 6 - (-1) = 7 feet.

Now, we'll calculate the area of the cross-section of the trough, which is the same as the area under the curve y = 1. The area under a constant function is equal to the value of the function multiplied by the length over which it extends. In this case, the area of the cross-section is 1 * 7 = 7 square feet.

To find the volume of water in the trough, we multiply the area of the cross-section by the height of the trough. The height is given as 1 foot. Therefore, the volume of water in the trough is 7 * 1 = 7 cubic feet.

Finally, we can calculate the amount of work required to empty the trough by multiplying the volume of water by the weight of water, which is 62 pounds per cubic foot. Thus, the amount of work required is 7 * 62 = 434 foot-pounds.

Therefore, the amount of work required to empty the trough by pumping the water over the top is 434 foot-pounds.

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The value of a that makes v⃗ parallel to w⃗ is a = -4

What is parallel?

"Parallel" refers to two or more lines, vectors, or objects that have the same direction and will never intersect. In the context of vectors, two vectors are parallel if they have the same or opposite direction. Parallel vectors can be scalar multiples of each other, meaning one vector can be obtained by multiplying the other vector by a constant factor.

To find the value(s) of a that make v⃗ = 4ai⃗ - 3j⃗ parallel to w⃗ = a2i⃗ + 3j⃗, we need to determine when the two vectors have the same direction, i.e., their direction vectors are scalar multiples of each other.

The direction vector of v⃗ is (4a, -3), and the direction vector of w⃗ is (a^2, 3). For these vectors to be parallel, their corresponding components must be proportional.

Therefore, we can set up the proportion:

(4a) / (a^2) = (-3) / 3

Simplifying this equation:

4a / a^2 = -3 / 3

Dividing both sides by a:

4 / a = -1

Cross-multiplying:

4 = -a

Solving for a:

a = -4

So, the value of a that makes v⃗ parallel to w⃗ is a = -4.

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Answer:

\(\frac{\sqrt{5} }{5}\)

Step-by-step explanation:

\(\frac{1}{\sqrt{5} }\)  multiply each side by \(\sqrt{5}\) which comes out to \(\frac{\sqrt{5} }{5}\)

Answer:

$8.50

Explanation:

Given the function f(h) that describes the total dollar amount Tomas earns, based on the number of hours he works:

When h=1, f(1)=250+8.5(1)=$258.5

When h=2, f(2)=250+8.5(2)=$267

Now:

It means therefore that for every additional hour, Tomas earns $8.5.

The hourly wage Tomas earns is $8.5.

Now,

1. The angles measures are larger than the original angle measures is a false statement.

2. If two sides parallel in the original figure, then those sides are parallel in the final figure is true statement.

3. The final angle measure are the same as the original angle measure is false statement.

4. The original figure and the final figure may not be congruent is true statement.

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The following is the answer to the given question:

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

Event of rolling the number 3: {3}

A sample space is a set or collection of potential outcomes from a random experiment. The letter "S" stands for the sample space in a symbol. The term "events" refers to a subset of possible experiment results. Depending on the experiment, a sample space may contain various outcomes. It is referred to as discrete or finite sample spaces if there are a finite number of possible outcomes.

The random experiment's sample spaces are written in curly braces, "{} ". The sample space and the events are distinct from one another. While the event can be written as {1, 3, 5,} which represents the set of odd numbers and {2, 4, 6,} which represents the set of even numbers, we will obtain the sample space, S, for rolling a die as {1, 2, 3, 4, 5, and 6}.

There are six faces to the cube, numbered 1 through 6. When the cube is rolled, one of the six faces—each bearing a number from 1 to 6—will be revealed, revealing the sample space. The event space is created similarly.

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Answer:

R= 30-9t.... I think

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

\(f(12)=\frac{3(12)+6}{7}=\boxed{6}\)

For any chi-square goodness-of-fit test, the number of degrees of freedom is equals to

(k - 1), where k is number of categories. So, second option is correct.

Chi-square goodness test : The chi-square goodness test is used to check whether the observed data distribution matches with the expected distribution. Since this is a non-parametric test, the data are divided into classes or groups, and the number of values that fall into those groups is compared to the expected number of values that fall into those groups. The chi-square test of goodness has

degrees of freedom equal to the number of groups minus one i.e., (k −1), where

k --> Number of classes or categories, the data is divided into.

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Answer:

1.321 then 0.008 is the same thing

Step-by-step explanation:

Given:

The average sale of a house decreased from $333,000 in February 2008 to $188,000 in February 2013.

Required:

To find the absolute change and the relative change.

Explanation:

The absolute change is

The relative change is

Final Answer:

Absolute change = -145,000

Relative change = -43.54%

Answer:

pi/4

Step-by-step explanation: