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Are the expressions (4c + 8) + 3c - 2 and 4c + 2(0.5c + 1) equivalent?

A: y=2x+3. This is an equation for the linear relationship in slope-intercept form. The equation states that the value of y is equal to the slope of the line, 2, multiplied by the value of x, plus 3.

Slope is a measure of the steepness of a line. It is the ratio between the vertical change in a line (change in y-values) over the horizontal change in the same line (change in x-values). It is also referred to as the rate of change, as it is a measure of how quickly the value of y changes with respect to the x-value.

This equation is used to describe a straight line that has a constant rate of change between two variables. This equation can be used to determine the slope, y-intercept, and x-intercept of a line.

The slope, which is the coefficient of x in the equation (2 in this case), is the rate at which y changes with respect to x. It is the rise over run, or the change in y over the change in x. The y-intercept is the value of y when x is equal to 0 (in this case, it is 3). The x-intercept is the value of x when y is equal to 0 (in this case, it is -3/2).

This equation is often used to represent a linear relationship between two variables, such as the amount of money a person earns in relation to the number of hours they work.

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The area of the shaded region in the standard normal distribution can be found to be 0.3510.

To find the area of the shaded region between -2.25 and -0.35 in a standard normal distribution, you would use a Z-table or a calculator with a built-in Z-table function.

Area between -2.25 and -0.35 = Area to the left of -0.35 - Area to the left of -2.25

Area to the left of -0.35 = 0.3632

Area to the left of -2.25 = 0.0122

find the difference between these two areas:

Area between -2.25 and -0.35 = 0.3632 - 0.0122 = 0.3510

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The correct number line is: A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.

The mathematical expression of a connection between two values, stating that one value is larger than, less than, or not equal to another value, is called an inequality. Common symbols for inequality include (less than), > (greater than), (less than or equal to), and (greater than or equal to). For instance, the inequality 2x + 3 > 7 denotes that the value of 2x + 3 is larger than 7. Depending on the circumstance, inequalities can be resolved algebraically or visually. A collection of values that meet the connection implied by the inequality is the answer to an inequality.

Here, the inequality is y - 2 < -5, which can be rewritten as y < -3.

Hence, the correct option is: A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.

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Answer:

To find the image of the point (7, 0) under the given translation, we apply the translation rule:

(x, y) → (x + 1, y - 2)

Substituting (7, 0) for (x, y), we get:

(7, 0) → (7 + 1, 0 - 2)

= (8, -2)

Therefore, the image of the point (7, 0) under the given translation is (8, -2).

So, the correct answer is (8, −2).

Step-by-step explanation:

hope its help <:

Answer:

Step-by-step explanation:

Because this problem is not easily solvable through factoring, we must use long division to find the answer.

      _______________                                                                                  x+7 | x3 + kx2 - 34x + 56

When performing long division on polynomials, we should try to cancel out the term with the greatest power first. So, we must figure out how many x's go into x3, because x is the first term of the first polynomial and x3 is the first term of the second polynomial. x*x2 = x3, so:

     x2

      _______________                                                                                  x+7 | x3 + kx2 - 34x + 56

  (-)  x3 + 14x2

         (k-14)x2 - 34x

Then, we see how many x's go into (k-14)x2. x*(k-14)x = (k-14)x2, so:

     x2 + (k-14)x

      _______________                                                                                  x+7 | x3 + kx2 - 34x + 56

  (-)  x3 + 14x2

         (k-14)x2          - 34x

    (-)  (k-14)x2 - 7kx - 98x

                        -7kx - 132x + 56= (-7k-132)x + 56

x*(-7k-132) = (-7k-132)x, so:

     x2 + (k-14)x + (-7k-132)

      _______________                                                                                  x+7 | x3 + kx2 - 34x + 56

  (-)  x3 + 14x2

         (k-14)x2          - 34x

    (-)  (k-14)x2 - 7kx - 98x

                        (-7k-132)x          + 56

                    (-) (-7k-132)x - 7k - 924

                                          -7k - 868

The answer is x2 + (k-14)x + (-7k-132) - [(7k-868)/(x+7)]

Answer:

28 people

Step-by-step explanation:

21 / 3 = 25

7 = 25%

25 x 4 = 100%

so

7 x 4 = 28

28 people are in the class

Answer:

The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14.

Substituting the given value of r=11 m and using π = 3.14, we get:

C = 2πr

C = 2 x 3.14 x 11 m

C = 69.08 m

Therefore, the circumference of the circle is 69.08 meters

Using the right cone formula we know that the surface area is 1281.77638m³ respectively.

An axis that is perpendicular to the base plane defines a right circular cone. By rotating a right triangle around one of its legs, we may create a right cone.

The right circular cone in the illustration has an axis that is perpendicular to the base and a circular base with a radius r.

So, the formula for the surface area of the right cone is as follows:

πr(r+√h²+r²)

We have the values: r = 13m and h = 13m

Now, insert values as follows:

= πr(r+√h²+r²)

= π13(r+√13²+13²)

= 1281.77638

Therefore, using the right cone formula we know that the surface area is 1281.77638m³ respectively.

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Three points on the graph: (4, 0), (13, 5), (28, 8)

What is function ?

Function can be defined in which it relates an input to output.

Function 1: y = [tex](x+2) ^{1/3}[/tex] - 1

Domain: x ≥ -2

Range: y ≥ -1

x-intercept: There is no x-intercept.

y-intercept: (0, -1)

Transformation: The cube root function is shifted 2 units to the left and 1 unit down.

Three points on the graph: (-2, -1), (-1, 0), (6, 1)

Function 2: y = 3[tex](x - 4)^{1/3}[/tex] + 2

Domain: x ≥ 4

Range: y ≥ 2

x-intercept: (4, 0)

y-intercept: There is no y-intercept.

Transformation: The cube root function is shifted 4 units to the right, vertically stretched by a factor of 3, and shifted 2 units up.

Therefore, Three points on the graph: (4, 0), (13, 5), (28, 8)

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Answer:2,160ft

Step-by-step explanation: Volume=length * width * height

30x8x9=2160

Answer:

To solve the problem, we can draw a number line and mark off the distances that Amiya jogged.

We start at 0 and mark off 1/3 of a mile to represent the distance Amiya jogged initially. Then we mark off another 1/3 of a mile to represent the distance she jogged after resting.

The total distance Amiya jogged is the distance from the starting point (0) to the end point (2/3), which is 2/3 of a mile.

Therefore, Amiya jogged a total of 2/3 of a mile.

Taking it further, to convert miles to meters, we need to know that 1 mile is equal to 1609.34 meters (approximately).

So to find out what 2/3 of a mile is in meters, we can multiply 2/3 by the conversion factor:

2/3 mile x 1609.34 meters/mile = 1072.89 meters

Therefore, 2/3 of a mile is approximately equal to 1072.89 meters.

A total possible number of bonuses awarded is given as follows:

6 bonuses.

The total number of bonuses awarded is obtained applying the proportions in the context of the problem.

The total amount of bonuses is of $5,000, and at least one $500 bonus and at least one $1000 bonus were awarded, hence the remaining amount to be awarded is of:

5000 - (500 + 1000) = $3,500.

For an amount of $3,500, a possible division of the bonuses is given as follows:

Hence a possible number of bonuses is given as follows:

2 + 1 + 3 = 6 bonuses.

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Answer:

86.96 inches.

Step-by-step explanation:

C = 2πr

d = 2r

Solving for C

C = πd = π · 28 ≈ 87.96459 inches

Answer:

i did this in 8th grade. (I'm homeschooled)

Step-by-step explanation:

Heres the best i got

Answer:

Step-by-step explanation:

Ici, nous allons réduire la fraction 18/25 aux termes les plus bas et la convertir en un nombre fractionnaire, si nécessaire.

Dans la fraction 18/25, 18 est le numérateur et 25 est le dénominateur.

On commence par trouver le plus grand diviseur commun de 18 et 25, qui est 1. Ensuite, on divise 18 et 25 par le plus grand diviseur commun pour obtenir la plus petite expression, écrite comme suit :

(18 ÷ 1) / (25 ÷ 1)

= 18/25

We cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.

The mean is a measure of central tendency that represents the average value of a set of numbers. It is also called the arithmetic mean or simply the average.

We cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.

The mean and the median are two different measures of central tendency, and they can have different values depending on the distribution of the data. In general, if a data set is symmetric and bell-shaped, the mean and the median are close to each other. However, if the data set is skewed, the mean and the median may be different.

For example, consider the following two data sets:

Set 1 data: 1, 2, 3, 4, and 5.

The median is 3.

The mean is (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3.

Data set 2: 1, 2, 3, 4, 10

The median is 3.

The mean is (1 + 2 + 3 + 4 + 10) / 5 = 20 / 5 = 4.

In data set 1, the mean is the same as the median. In data set 2, the mean is greater than the median because the value 10 is an outlier that pulls the mean up.

Therefore, without additional information about the distribution of the data, we cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.

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Answer:

  (a)  Figure 3

  (b)  66.2 meters per second

Step-by-step explanation:

You want to know the figure that shows the best fit of a curve to the data, and you want to know the value of the curve when x = 8 seconds.

The fit is best when the difference between the data points and the curve is minimized. Often the sum of the squared differences is the metric that is minimized when the fit is best.

The gaps between the data points and the curve shown are greatest in Figures 1 and 2, so Figure 3 has the best fit.

The speed is estimated by the equation of the curve of best fit as ...

  y = 0.6x² +2.1x +11

A slight rearrangement can make this easier to evaluate:

  y = (0.6x +2.1)x +11

For x=8, the value of y is ...

  y = (0.6·8 +2.1)·8 +11 = 6.9·8 +11 = 66.2

The predicted speed at 8 seconds is 66.2 meters per second.

Answer:

The answer is 40% :) Hope this helps!

The expression that could be used to predict the number of ants on the banana peel after n minutes is given as follows:

5 + 7n.

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant, being called common difference d.

The nth term of an arithmetic sequence is given by the explicit formula presented as follows:

[tex]a_n = a_1 + (n - 1)d[/tex]

In this problem, the difference between consecutive terms is of 7, meaning that it represents an arithmetic sequence with a common difference of 7.

The first term is of 12, hence we obtained the explicit formula as follows:

12 + 7(n - 1) = 12 + 7n - 7 = 5 + 7n.

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Answer: It is 18.62 or c

Step-by-step explanation:

The parallelogram ABCD's congruency can be proven using Side-Angle-Side (SAS) congruence theorem.

Prove that ΔABC ≅ ΔDCB using the Side-Angle-Side (SAS) congruence theorem.

Given that ABCD is a parallelogram, AB || CD and BC || AD. Therefore, ∠ABC ≅ ∠DCB and ∠ACB ≅ ∠DCA because they are corresponding angles.

AB ≅ CD and BC ≅ AD because opposite sides of a parallelogram are congruent.

Lastly, AC ≅ AC because it is a shared side between the two triangles.

Therefore, the following congruent parts:

∠ABC ≅ ∠DCB (by corresponding angles)

AB ≅ CD (by opposite sides)

BC ≅ AD (by opposite sides)

AC ≅ AC (shared side)

The SAS congruence theorem concludes that ΔABC ≅ ΔDCB.

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Image transcribed:

Prove ΔABC ≅ ΔDCB

Answer:

b=7 & c=7√2

Step-by-step explanation:

b=7 as it is an isosceles triangle

now using Pythagoras theorem,

(c)^2= (7)^2+(7)^2

⇒(c)^2= 49+49

⇒(c)^2= 98

⇒c= √98

⇒c=7√2

Answer:

Step-by-step explanation:

You want the missing side lengths in an isosceles right triangle with one side given as 7.

The two congruent acute angles tell you this right triangle is isosceles. That means sides 7 and b are the same length:

  b = 7

The hypotenuse of an isosceles right triangle is √2 times the side length:

  c = 7√2

__

Additional comment

You can figure the hypotenuse using the Pythagorean theorem if you haven't memorized the side relations of this "special" right triangle.

  c² = 7² + b²

  c² = 7² +7² = 2·7²

  c = √(2·7²) = 7√2

The side length ratios for an isosceles right triangle (angles 45°-45°-90°) are 1 : 1 : √2.

The other "special" right triangle is the 30°-60°-90° triangle, which has side length ratios 1 : √3 : 2.

Therefore , the solution of the given problem of unitary method comes out to be  the gas particles inside the can will acquire kinetic energy and collide with its walls more frequently, increasing pressure.

The objective can be accomplished by variable use of what has been clearly learned thus far, implementing advantage of this worldwide convenience, and incorporating all essential components from prior flexible research that used a specific approach. If the anticipated claim outcome actually occurs, it will be feasible to get in connection with the entity once more; if not, both crucial systems will undoubtedly miss the statement.

Here,

The pressure of the gas inside the can will rise as the temperature rises. This is due to the fact that the gas particles inside the can will accelerate and acquire kinetic energy, causing them to collide with the can's walls more frequently and more violently.

The pressure rises as a result of these collisions' greater power per unit area.

The Ideal Gas Law, which says that PV = nRT, where P is tension, V is volume, n is the number of moles of gas,

R is the optimal gas constant, and T is temperature in Kelvin, describes this relationship between pressure and temperature.

In conclusion, the Ideal Gas Law predicts that as the temperature inside the vehicle rises, the gas particles inside the can will acquire kinetic energy and collide with its walls more frequently, increasing pressure.

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Answer:

2n + 14 = 30

Step-by-step explanation:

Since you know that 2n + 14 = 30, we can determine the values by first subtracting 14 from 30. Our equation would then be 2n = 16. Divide 2 from both sides and n = 8.

This model represents the total on the top and the 2 parts on the bottom.

Answer:

Yes, ∆PQR is a right triangle.

Step-by-step explanation:

A right triangle has one right angle, which is 90°. This triangle has one right angle, so it is a right triangle.

No, Sophia is not correct. While we can see that Morgan had more total weight overall in their two week recycling data, we can't say for sure that Morgan's data is greater without calculating the exact numbers.

Recycling data is information collected from the recycling process that is used to measure and analyze the effectiveness of the process. This data can include the type and amount of materials collected, the location of collection, the method of collection, and the end-use of recycled materials. Recycling data can be used to help identify areas for improvement, develop innovative recycling solutions, and evaluate the impact of current programs. It can also be used to understand consumer behavior and inform decisions on waste management. By collecting and analyzing recycling data, governments, businesses, and organizations can better understand how to reduce waste and increase the reuse and recycling of materials.

We need to calculate the means of the data to determine which one is larger.

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Answer:

Step-by-step explanation:

70% of 140 is equal to 0.7 x 140 = 98. Therefore, the answer is 98.

Answer:

98

Step-by-step explanation:

70% can also be written as 0.7, therefore, we can multiply 140 by 0.7.

140 x 0.7 = 98.

Therefore , the solution of the given problem of percentage comes out to be the firm expects that each warranty it sells will be worth $1.41.

In statistics, "a%" is used to refer to a figure or number that is expressed as a percentage of 100. Additionally rare are the forms that "pct," "pct," or "pc". It is typically represented by the symbol "%," though. Additionally, there are not any indicators and the proportion of each item to the overall amount is flat. Since percentages typically add up to 100, they are essentially integers. Either the expression "fraction" or the symbol for percentage (%) .

Here,

The price to substitute each item is $200. The anticipated price for each component is thus:

Expected cost per product equals Replacement cost x Failure Probability

=> Cost per product anticipated = 0.008 x $200

=>  Expected price per item is $1.60.

So, the following is the anticipated value of each warranty sold:

Expected worth of the warranty = Failure rate x (Replacement cost - Cost of warranty)

=>   Expected guarantee value = 0.008 * ($200 - $22 - $1.60).

=>  Expected guarantee value = 0.008 * $176.40

=>  Expected warranty worth is $1.41

As a result, the firm expects that each warranty it sells will be worth $1.41.

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The option that describes the null and alternative hypothesis, test statistic and conclusion will be B. test statistic = -1.5625 and the conclusion is to reject the null hypothesis.

In statistical hypothesis testing, the null hypothesis (H0) is a statement that assumes no significant difference or relationship between two or more variables. It represents the default position that there is no effect or change, or that any observed effect is due to chance.

The alternative hypothesis (H1), on the other hand, represents the opposite of the null hypothesis. It states that there is a significant difference or relationship between the variables being tested. The alternative hypothesis is typically what the researcher is trying to prove or support with their study.

The test statistic will be:

= (116 - 121) / 16(✓1/50 + 1/50)

= -1.5625

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