Unit: Real Numbers


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Question ID: 501911


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Consider the calculation x – y +( – z) where x and z are positive real numbers and y is a negative real number.


i) What are the directions of motion for this calculation?


ii) Is the final answer positive, negative, or undetermined?


i) Right, right, left


ii) Undetermined


i) Right, right, left


ii) Positive


i) Right, left, left


ii) Undetermined


i) Right, left, left


ii) Negative

From the given information provided, the approximate volume of the cone is 94.24777 cubic inches.

The volume of a cone can be calculated using the formula V = (1/3) × π × r² × h, where "r" is the radius of the base of the cone, "h" is the height of the cone, and "π" is the mathematical constant approximately equal to 3.14159.

Radius r= 3 inches

Height h= 10 inches

π = 3.14159

Using the formula for the volume of a cone, V = (1/3) × π × r² × h, we can substitute the given values to calculate the volume of the cone:

V = (1/3) × 3.14159 × 3² × 10

V ≈ 94.24777 cubic inches

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\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

Here we go ~

\(\qquad \sf  \dashrightarrow \: 4(1 - 5x) + 2 \leqslant 166\)

\(\qquad \sf  \dashrightarrow \: 4 - 20x + 2 \leqslant 166\)

\(\qquad \sf  \dashrightarrow \: - 20x + 6\leqslant 166\)

\(\qquad \sf  \dashrightarrow \: - 20x \leqslant 166 - 6\)

\(\qquad \sf  \dashrightarrow \: - 20x \leqslant 160\)

\(\qquad \sf  \dashrightarrow \: - x \leqslant 160 \div 20\)

\(\qquad \sf  \dashrightarrow \: - x \leqslant 8\)

\(\qquad \sf  \dashrightarrow \: x \geqslant 8\)

[ Inequality changes as we multiply -1 on both sides ]

To keep away from the construct of a dummy variable and perfect multicollinearity, it is pertinent to omit one of the dummy variables. Inclusion of one fewer dummy variable than the categories present in the variable permits for estimation of the intercept term, and thereby, a valid model that is capable of offering predictions.

In a linear regression model, categorical variables (factors) can be represented by making one or more dummy variables. Let's say that the categorical variable is color, with 'red', 'blue' and 'green', two dummy variables may be created - one for blue and another for green. Typically, the reference category is the one not included in the model; in this case, it would be red.

If all the dummy variables are included as part of the linear regression model that contains an intercept term, it may lead to a situation called "dummy variable trap". The sum of these dummy variables is equal to the intercept term and thus causes perfect multicollinearity which results in inaccurate coefficients due to which the whole model becomes impossible to use.

For instance, if color possesses three categories then two dummy variables should be produced for blue and green. The coefficient of these dummy variables point out to the variance between the reference categorization and two further categories symbolized by the dummy variables.

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Mr. Steiner will need to pay $18774 in total and he paid $4774 more than the actual price of the car.

we know that the amount of money earned, in compound interest after t years is showed as, A(t) = P (1+\(\frac{r}{n}\))ⁿ\(^{t}\)

here, we know that A(t) is the amount of money after t years.

P is the initial sum of money, know as principal,

r is the interest rate as a decimal value,

n is the number of times that interest is compounded per year,

and

t is the time in years for which the money is invested or borrowed.

now here we know,

P = 14000, r = 0.049, n = 12, t = 6

when we have all values we can find,

A(t) = P(1+\(\frac{r}{n}\))ⁿ\(^{t}\)

A(6) = 14000 (1+\(\frac{0.049}{12}\))¹²ˣ⁶

A(6) = 18774

therefore we know that Mr. Steiner needs to pay $18774 in total.

now,

18774 - 14000 = 4774

therefore we get to know that Mr. Steiner paid $4774 more than the actual price of the car.

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The multiplier that would be used to calculate the depreciation of the car is 0.83^y.

Depreciation is when the value of an asset declines due to wear and tear.

The equation that can be used to represent depreciation is:

Value of the asset x (1 - rate of depreciation)^years

$31,000 x 0.83^y.

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Answer: y= -x+7

Step-by-step explanation: Use the formula (y2-y1)/(x2-x1) to find slope. (3-(-2))/(4-9) equals 5/-5. The slope of this equation is -1. Next, plug in 4 for x and 3 for y. 3=(-1)(4)+b. 3=-4+b, so b =7.

The center of the circle is (-2, -4) and the radius of the circle is sqrt(75).

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

\((x-h)^2 + (y-k)^2 = r^2\)

We are given that;

The equation; x² + y² + 4x+8y-55= 0

We can rewrite the given equation in the standard form for the equation of a circle:

(x² + 4x) + (y² + 8y) = 55

Completing the square for both x and y, we can rewrite this as:

(x² + 4x + 4) + (y² + 8y + 16) = 55 + 4 + 16

Simplifying, we get:

(x + 2)² + (y + 4)² = 75

Now we can identify the center and radius of the circle. The center of the circle is given by (-2, -4), which is the opposite of the coefficients of x and y in the completed square form of the equation. The radius of the circle is given by the square root of the constant term on the right-hand side of the equation, which is sqrt(75).

Therefore, by the given equation of circle answers will be (-2, -4) and sqrt(75).

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Answer:

2,075 = 5 × 5 × 83

√2,075 = 5√83 = about 45.55

A graph which represents the overall equation (inequality) represented by this scenario is shown in the image attached below.

A graph can be defined as a type of chart that is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).

Let the variable x represent the total number of guests.

Let the variable y represent the amount of meat

Next, we would write an inequality that represents an amount of meat that must be 2 pounds fewer than one-third (1/3) the total number of guests. Since the customer decides they want at least that amount of meat, the inequality symbol that must be used is greater than (>).

y > 1/3(x) + 2

y > x/3 + 2

In conclusion, the y-value for this inequality graph (see attachment) intersects the x-axis at 0 and 6 with the boundary line shaded upward and dashed to indicate that it is not part of the solution, which must be represented with a greater than (>) inequality symbol.

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ANSWER

zeros: (0, 0), (2, 0), (3, 0), (-1, 0)

The correct graph is option A

EXPLANATION

Answer:

Part A

= 9 flowers

Part B

= 5 flowers

Step-by-step explanation:

Emily has 59 flowers. She wants to put the flowers in 6 vases with the same number in each vase.

Part A: What is the greatest number of flowers she can put in each vase?

This is calculated as:

59 flowers ÷ 6 vases

= 9 5/6 flowers

Therefore, the greatest number of flowers she can put in each vase is 9 flowers

Part B: How many flowers will Emily have left over?

We have to calculate the number of flowers in the 6 vases above

= 9 flower × 6

= 54 flowers

Hence:

= 59 flowers - 54 flowers

= 5 flowers

Therefore, Emily would have 5 flowers left over.

Answer:

Step-by-step explanation:

a

Answer:24

Step-by-step explanation:

71 + 25=96

96 divided by 4 equals 24

you have to add her profit and her expenses to see how much she needed to sell

We identify the proportional relationship because it does not have a constant term, the correct option is:

y = (1/4)x

A proportional relationship between two variables x and y is written as:

y = k*x

Where k is called the constant of proportionality.

Here the options are:

The only option that has not a constant term is the second one:

y = (1/4)*x

And that is the proportional relationship.

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Answer:

y=(1/4)x

Step-by-step explanation:

I took the test :)

Answer:

541686

Step-by-step explanation:

678,686-137,000=541686

A scientist might set a lower significance level to reduce the likelihood of a Type I error (false positive) and increase the confidence in their results.

When conducting a hypothesis test, a scientist uses statistical methods to evaluate the evidence for or against a proposed hypothesis.

The significance level of a hypothesis test is the probability of rejecting the null hypothesis when it is true, which is also known as a Type I error. In other words, a significance level of 0.05 means that there is a 5% chance of rejecting a true null hypothesis, and accepting a false alternative hypothesis.

Setting a lower significance level, such as 0.01, means that the scientist is willing to accept a higher level of confidence in their results and reduce the likelihood of making a Type I error.

This means that the researcher is willing to accept that there is only a 1% chance of rejecting a true null hypothesis, which is a more conservative approach.

There are several reasons why a scientist might choose to set a lower significance level.

First, if the consequences of a false positive are severe or costly, such as in medical research or engineering, then a lower significance level can help to minimize the risk of making a wrong decision.

Second, if the sample size is small, a lower significance level can help to reduce the impact of random variation and increase the confidence in the results.

Finally, if the effect size of the study is small, a lower significance level can help to ensure that the observed difference is not due to chance and is truly meaningful.

In summary, setting a lower significance level can help a scientist to increase the confidence in their results, reduce the likelihood of making a Type I error, and ensure that the observed difference is not due to chance.

However, it is important to balance the need for a high level of confidence with the practical considerations of the study and the potential consequences of a false positive.

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Answer:

17

Step-by-step explanation:

5+T(6-3); T=4

Use order of operations. Parenthesis, multiplying, then add last.

= 5 + 4(6 -3)

= 5 + 4(3)

= 5 + 12

= 17

Answer:

x=13/33 and y=12/33

Step-by-step explanation:

x=13/33 and y=12/33

Answer: $3,400

Step-by-step explanation:

Juanita owes $7,000, she pays $150 a month for two years.

Step 1: Create an equation we can plug our values into

7,000=150x +b ------> x=# of months --------> b=what is still owed

There are 12 months in a year. 12(2)=24

7,000=150(24)+b

7,000=3600 +b

-3600 -3600

$3,400=b

Answer:

60

Step-by-step explanation:

n/2 + 5 = 35

N/2 = 30

N = 60

The brewed coffee has 80 mg  , red bull energy drink has 80 mg and mountain dew soda has 37 mg of caffeine .

In the question ,

it is given that the 1 serving contain total of 197 mg of caffeine

let the amount of caffeine in 1 serving of brewed coffee be "c"

let the amount of caffeine in 1 serving of red bull energy drink  be "e"

let the amount of caffeine in 1 serving of mountain dew soda be "s"

So , c + e + s = 197

also given that

one serving of brewed coffee has 6mg more than two servings of mountain dew, which means

c = 2s + 6

and one serving of red bull contains 37 mg less caffeine than the total amount of caffeine in one serving each of brewed coffee and mountain dew ,which means

e = c + s - 37

Substituting the values in the equation c + e + s = 197  ,

we get

2s + 6 + c + s - 37 + s = 197

2s + 6 + 2s + 6 + s - 37 + s = 197

6s -25 = 197

6s = 222

s = 222/6

s = 37

So , c = 2(37) + 6 = 80

e \(=\) 37 + 80 - 37 = 80

Therefore , The brewed coffee has 80 mg  , red bull energy drink has 80 mg and mountain dew soda has 37 mg of caffeine .

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Answer:

a

Step-by-step explanation:

To prove that triangle FGE and triangle IJH we need information like the two sides of each triangle and the included angle to be congruent.

To prove two triangles are similar by the SAS is that you need to show that two sides of one triangle are proportional to two corresponding sides of another triangles, with the included corresponding angles being congruent.

For the SAS postulate you need two sides and the included angle in both triangles.

Side-Angle-Side (SAS) postulate:-

If two sides and the included angles of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. SAS postulate relate two triangles and says that two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

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Answer:

Negative line/slope

Step-by-step explanation:

Slope format: y = mx + b

If the slope (mx) is negative, then the slope of the line is negative

The area of the region enclosed by the petal of a rose curve r = sin2θ in the first quadrant is π/8 square units

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We know the area in the polar coordinates is given by:

\(\rm A =\int\limits^a_b {\dfrac{1}{2}r^2} \, d\theta\)

We have r = sin2θ

Here the quadrant is not given, so we are assuming we need to find the area in the first quadrant.

Put this value in the above integration and limit 0 to π/2

\(\rm A =\int\limits^{\dfrac{\pi}{2}}_0 {\dfrac{1}{2}(sin^22\theta)} \, d\theta\)

After solving the above integration, we get:

\(\rm A = \dfrac{\pi}{8}\)

Thus, the area of the region enclosed by the petal of a rose curve r = sin2θ in the first quadrant is π/8 square units

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