9. (06.06 MC)
A student attempted to generate an equivalent expression using the distributive property, as shown below:
2(x+5) = 2x+5
What was the mistake made? (5 points)
1.Incorrect sign was used for the second term

2.2 was not multiplied by 5

3.2 was not multiplied by x
Incorrect sign was used for the first term

Answer:

8 pints=4 quarts,16 cups is 8pints

Step-by-step explanation:

It is multiplication, if you write it down then think about how the numbers connect its easier to understand.

Answer:

[tex]y = \frac{1}{7} x + 5[/tex]

Step-by-step explanation:

[tex]x - 7y = - 21[/tex]

[tex] - 7y = - x - 21[/tex]

[tex]y = \frac{1}{7} x + 3[/tex]

The probability that exactly 7 employees out of 23 sent complete the program is 0.217 or 21.7%.

In this case, the number of trials is 23, and the probability of success is 0.4 (since, on average, 40% of those sent complete the program). We want to find the probability of exactly 7 successes.

The binomial probability formula is:

P(X=k) = [tex](^n_k) \times p^k \times (1-p)^{(n-k)}[/tex]

Where P(X=k) is the probability of k successes, n is the total number of trials, p is the probability of success, and (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials.

Using this formula, we can calculate the probability of exactly 7 employees completing the program as follows:

P(X=7) = [tex](^{23} _7) \times 0.4^7 \times (1-0.4)^{(23-7)}[/tex]

= 0.217 or 21.7%

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In conclusion, the determinant of M being non-zero only guarantees that the equation has a unique solution, but it does not guarantee that it has a solution for every value of A.
If the determinant of M is not equal to zero, then A can be solved in terms of X or X can be solved in terms of A. This is because the matrix M is invertible when its determinant is non-zero. In other words, the matrix M has a unique inverse.
Here are the statements that are correct:
- Given any X, there is one and only one A which will satisfy the equation. This is because when the determinant of M is non-zero, the matrix M is invertible, and hence the equation can be uniquely solved for A in terms of X or for X in terms of A.
- Some values of A (such as A=0) will allow more than one X to satisfy the equation. This is because the determinant of M being non-zero only guarantees that the equation has a unique solution, but it does not guarantee that it has a solution for every value of A.
- Some values of X will have more than one value of A that satisfy the equation. This is true for any equation that has multiple solutions, regardless of the determinant of M.
- Some values of A will have no values of X that satisfy the equation. This is true for any equation that has no solution, regardless of the determinant of M.
- There is no value of X which satisfies the equation when A=0. This is because when A=0, the equation reduces to 0=0, which is true for any value of X.

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Answer:

1.   No, the side lengths 3, 5, and 9 cannot make a triangle.

2.  If you are scaling an object by ¹/₃, it makes the object smaller.

     If the real object is 30 inches long, it is 10 inches once it is scaled.

3.  A cube has 6 faces.

     To find the volume, cube the side length:  6³ = 216 in³

Step-by-step explanation:

According to the Triangle Inequality Theorem, the sum of any two sides of a triangle is greater than the length of the third side.

As the sum of the two sides measuring 3 and 5 is 8, and 8 is not greater than 9, the side lengths 3, 5, and 9 cannot make a triangle.

Scaling an object reduces or enlarges its size. When scaling an object:

Therefore, if you are scaling an object by ¹/₃, the object becomes smaller, since ¹/₃ is between zero and 1.

To scale length, simply multiply the length by the scale factor.

Therefore, if a real object is 30 inches long, its length once it is scaled is:

[tex]\implies \sf 30 \times \dfrac{1}{3}=\dfrac{30}{3}=10\;inches[/tex]

A cube is a three-dimensional solid shape with six square faces.

The volume of a cube is the product of its width, length and height.

If the side of a cube measures 6 inches, its volume is:

[tex]\begin{aligned}\implies \sf Volume &=\sf 6 \times 6 \times 6 \\&= \sf 36 \times 6 \\&= \sf 216\;in^3\end{aligned}[/tex]

Answer:

See below, please.

Step-by-step explanation:

Ans 1.

In order to make a triangle, three line segments are needed, and the sum of the lengths of any two sides must be greater than the length of the remaining side. The side lengths 3, 5, and 9 cannot make a triangle because 3 + 5 is less than 9, which violates the triangle inequality.

Ans 2.

Scaling an object by 3 makes the object larger, as each dimension (length, width, and height) is multiplied by 3. If the real object is 30 inches long and is scaled by 3, it will be 90 inches long.

Ans 3.

A cube has 6 faces. To find the volume of a cube when one side measures 6 inches, we use the formula V = s^3, where s is the length of one side. Plugging in s=6, we get V = 6^3 = 216 cubic inches.

Certainly, there is a significant difference in the mean amount of e.coli bacteria detected by the two methods for this type of beef. This can be supported statistically by conducting a hypothesis test.

           The null hypothesis ([tex]H_0[/tex]) is that there is no significant difference in the mean amount of E. coli bacteria detected by the two methods. The alternative hypothesis ([tex]H_a[/tex]) is that there is a significant difference in the mean amount of e.coli bacteria detected by the two methods.

          The two-sample t-test can be used to test the hypothesis. The t-test compares the means of two independent groups and determines whether they are significantly different. The t-test assumes that the two samples are normally distributed and have equal variances.

          If the sample sizes are large, then the t-test can still be used even if the samples are not normally distributed.

          The formula for the t-test is:

                   [tex]t = (x_1 - x_2) / [s^2(1/n_1 + 1/n_2)][/tex]

       Where:

                     [tex]x_1[/tex] = the sample mean for method 1

                     [tex]x_2[/tex] = the sample mean for method 2

                     [tex]s^2[/tex] = the pooled variance of the two samples

                     [tex]n_1[/tex] = the sample size for method 1

                     [tex]n_2[/tex] = the sample size for method 2

        The t-value can then be compared to the critical value of  [tex]t[/tex] for the desired level of significance (usually 0.05).

         If the t-value is greater than the critical value of [tex]t[/tex], then the null hypothesis can be rejected and it can be concluded that there is a significant difference in the mean amount of E. coli bacteria detected by the two methods.

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To convert Wendall's measurements from inches to feet, we need to divide each measurement by 12, since there are 12 inches in a foot. So, the measurements in feet are:Length (in)Length (ft)242363484605To convert Stacey's measurements from feet to inches, we need to multiply each measurement by 12. So, the measurements in inches are:Length (ft)Length (in)6727848969108Therefore, the measurements of the wooden planks Wendall measured in feet are 2, 3, 4, and 5 feet, and the measurements of the wooden planks Stacey measured in inches are 72, 84, 96, and 108 inches.

Answer
Y. Answer:

y=30

Step-by-step explanation:

(3)^2 equals 9, so the first blank is 9.

You then multiply it by the 2, so second blank is 18.

18+15=33

33-3=30=y

Answer:

30

Step-by-step explanation:

first space should be 9 since 3² is 9

second space should be 18 since 2×9=18

final space should be 30 since 18+15 is 33-3=30

The four uppercase letters of the alphabet in block style with rotational symmetry are H, I, O, and X. Rotational symmetry refers to the property of a figure or object that appears identical after being rotated around a central point by a certain angle.

In block style writing, letters are written with straight lines and sharp corners, creating a uniform and geometric appearance. H, I, O, and X are the only uppercase letters that have rotational symmetry and can be written in block style.

H has a rotational symmetry of 180 degrees, meaning it looks the same when rotated 180 degrees around its center point.

I has a rotational symmetry of 180 degrees as well, with the dot above the letter acting as its center point.

O has a rotational symmetry of 360 degrees, meaning it looks the same when rotated any number of degrees around its center point.

Lastly, X has a rotational symmetry of 180 degrees, with the intersection of the two lines acting as its center point.

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Option a) The finding that the reputation of lawyers with the general public has declined because of advertising is NOT supported by several studies about lawyer advertising.

Lawyer advertising refers to advertising or soliciting the services of lawyers. It is designed to attract potential clients to retain their services. Lawyer advertising may involve a wide variety of mediums, including television, radio, print media, billboards, and the internet. Legal professionals may advertise their services on a wide range of platforms in order to reach as many people as possible.

According to several studies about lawyer advertising, the public considers the ads a valuable source of information. However, the public objects when advertising is invasive. The findings show that the negative effects of lawyer advertising on the reputation of lawyers with the general public are not supported by empirical data. In other words, the reputation of lawyers with the general public has not declined because of advertising.

The following are some of the other findings of several studies about lawyer advertising:

However, the public also perceives lawyer advertising as an attempt to lure them into hiring a lawyer. Lawyer advertising can increase public awareness about the availability of legal services, but it can also lead to unrealistic expectations regarding the outcome of legal disputes.

Hence option a) is correct.

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The arithmetic mean return is 3.6%, and the standard deviation is 2.14%.

To find the arithmetic mean, we add up the five returns and divide by the number of returns (in this case, 5):

(3% + 6% + 0% + 6% + 3%) / 5 = 3.6%

To find the standard deviation, we first need to find the variance. We can do this by taking each return, subtracting the mean return (3.6%), squaring the result, summing these values, and dividing by the number of returns minus 1 (4 in this case):

((3% - 3.6%)^2 + (6% - 3.6%)^2 + (0% - 3.6%)^2 + (6% - 3.6%)^2 + (3% - 3.6%)^2) / 4 = 0.046

The standard deviation is the square root of the variance:

√0.046 = 0.214 or 2.14%

Therefore, the arithmetic mean return for security y is 3.6%, and the standard deviation (sample) is 2.14%.


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R carries inversely as the cube S . If R=9 when S=3 ,  S= 4, when R= 243÷64.

Inverse proportionality is a mathematical relationship between two variables, in which an increase in one variable leads to a decrease in the other variable in such a way that their product remains constant. In other words, if the value of one variable is multiplied by a certain factor, the value of the other variable will be divided by the same factor.

Mathematically, two variables x and y are said to be inversely proportional if their relationship can be expressed as:

x * y = k

where k is a constant, and the symbol * denotes multiplication.

For example, the distance travelled by a car is inversely proportional to the time taken to travel that distance, assuming the car maintains a constant speed. If we let d represent the distance travelled and t represent the time taken, then we can express their relationship as:

d * t = k

where k is a constant

If R varies inversely as the cube of S, then we know that:

R ∝ [tex]\frac{1}{S^{3} }[/tex]

We can express this relationship using a proportionality constant k:

R = [tex]\frac{k}{S^{3} }[/tex]

To find the value of k, we can use the given information that R = 9 when S = 3:

9 = [tex]\frac{k}{3^{3} }[/tex]

9 = [tex]\frac{k}{27 }[/tex]

k = 9 * 27

k = 243

Now we can use this value of k to find S when R = [tex]\frac{243}{64}[/tex]:

[tex]\frac{243}{64}=\frac{243}{S^{3} }[/tex]

Simplifying this equation, we get:

S³ = [tex]\frac{243*64}{243}[/tex]

S³ = 64

S = ∛64

S = 4

Therefore, when R = [tex]\frac{243}{64}[/tex], S = 4.

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Answer: i am certain that the answer is -6

Answer:

Step-by-step explanation: Since the rectangle sits within the larger circle, let's look at it this way:

Area of Shaded Region = Area of Circle - Area of Rectangle

OR

(X) =( pi * r^2 ) - (rectangle length * rectangle width)

Now we fill in the numbers where we know the numbers:

(X) = (pi * (12 cm)^2) - (3cm * 10cm)

(X) = (pi * 144cm^2) - (30 cm^2)

(X) = 144pi - 30

(X) = 452.39 - 30

(X) = 422.39 cm^2

The line of sight distance using the angle of depression 13° is derived to be 2222.71 m to the nearest hundredth meters.

The angle of depression is an angle formed between the horizontal line and the line of sight when an observer looks downwards.

Considering the right triangle formed by the height of the tower and the complementary angle 77°, we shall represent the line of sight distance for the television camera to the base of the stadium with x so that;

cos 77° = 500/x {adjacent/hypotenuse}

note that 90° - 13° = 77°

x = 500/ cos 77° {cross multiplication}

x = 2,222.7057.

Therefore, the line of sight distance for the television camera to the base of the stadium to the nearest hundredth meters is equal to 2,222.71. Using the trigonometric ratio of cosine for the angle 77° which is complementary to the angle of depression 13°

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The answer is 1570. To evaluate the expression 547+233×5−142, we need to follow the order of operations, which is PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction).

There are no parentheses or exponents, so we start with multiplication and division from left to right.

233×5 = 1165

Then, we can simplify the expression to:

547 + 1165 - 142

Next, we add and subtract from left to right:

547 + 1165 = 1712

1712 - 142 = 1570

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Answer:

500 meters.

Step-by-step explanation:

The statement that best describes the use of spaces in folders and files names in ArcGIS is "Using spaces in folder and file names in ArcGIS is permitted but strongly discouraged."

ArcGIS is a geographic information system software that is used for creating, editing, analyzing, and sharing spatial data. The software is widely used by GIS professionals, environmental scientists, geographers, and other experts to manage and analyze spatial data.

In ArcGIS, it is possible to use spaces in folder and file names, but it is not recommended. This is because spaces can cause problems when the software tries to access files with spaces in their names. Therefore, it is better to use underscores or hyphens instead of spaces when naming folders and files in ArcGIS. This helps to avoid issues when working with data in ArcGIS.
The statement "Using spaces in folder names in ArcGIS is permitted but strongly discouraged" is the best description of the use of spaces in folder and file names in ArcGIS.

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Answer: B)

The recursive formula for the sequence 25, 5, 1,… is a(1) = 25 and a(n) = 5 * a(n-1) for n > 1.

Step-by-step explanation:

This is because each term is 1/5 of the previous term. So, the sequence is a(1) = 25, a(2) = 5, a(3) = 1, a(4) = 1/5, a(5) = 1/25, and so on. Does that help?

The scale factor that takes the segment of length l to the segment of length n is 2.25.

Length is a measurement of the distance between two points, usually expressed in units such as inches, feet, yards, meters, and kilometers. It is used to measure the size of objects, the distance between objects, and the length of a path or route. Length is one of the four fundamental units in the metric system, along with mass, time, and temperature.

This can be determined by a process of successive scaling. The initial segment of length l is first scaled by a factor of 1.5 to give a segment of length m. This segment is then scaled by a factor of 1.5 to give a segment of length n. Multiplying the two scaling factors together, 1.5 x 1.5, gives 2.25, which is the scale factor from the initial segment of length l to the final segment of length n.

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The scale factor that takes the segment of length l to the segment of length n is 2.25.

Length is a measurement of the distance between two points, usually expressed in units such as inches, feet, yards, meters, and kilometers. It is used to measure the size of objects, the distance between objects, and the length of a path or route. Length is one of the four fundamental units in the metric system, along with mass, time, and temperature.

This can be determined by a process of successive scaling. The initial segment of length l is first scaled by a factor of 1.5 to give a segment of length m. This segment is then scaled by a factor of 1.5 to give a segment of length n. Multiplying the two scaling factors together, 1.5 x 1.5, gives 2.25, which is the scale factor from the initial segment of length l to the final segment of length n.

To calculate the scale factor that takes the segment of length l to the segment of length n, the following formula can be used:
n = (1.5)²×l
Therefore, the scale factor is (1.5)² = 2.25. This means that the segment of length l needs to be scaled by a factor of 2.25 in order to produce the segment of length n.

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According to combinations formula there are 495 possible committees that can be selected from a group of 12 people.

To calculate this, you can use the formula for combinations

nCr = n!/(r!(n-r)!)

where n is the total number of people (12) and r is the number of people on the committee.
Therefore, the possible number of committees that can be selected is;

= {12!}/{4!8!}
= 12*11*10*9/4*3*2*1

= 11880/24
= 495
Therefore, 495 possible committees can be selected from a group of 12 people if a committee of 4 is to be selected.

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Answer: 28x+8y+2

Step-by-step explanation:

Remove parentheses: -2(14x-4y-1)

Solution: 28x+8y+2

Answer:

28x+8y+2

Step-by-step explanation:

The overall height of the framed picture is 89cm in the total.

The mount is 6 cm across the top and sides and 9 cm across the bottom. As a result, the mount's overall height will be:

45 cm = 6 cm (top) + 30 cm (image height) + 9 cm (bottom).

The mount's entire breadth will be:

6 cm (left) + 40 cm (width of the image) + 6 cm (right) = 52 cm

To get the total height of the framed image, multiply the height of the mount by the height of the picture by twice the width of the frame (since the frame goes around all four sides of the picture).

As a result, the overall height of the framed image will be:

45 centimetre plus 40 cm plus 2(2 cm) Equals 89 cm.

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Answer:

Approximately 1.05 × 10⁹ pounds of food are consumed by African elephants in one day.

Step-by-step explanation:

Answer:

Step-by-step explanation:

its 7 or 6\

The amount of gas Karen has and the amount Karen needed to put into her boat obtained using basic arithmetic operations are;

Basic arithmetic operations include addition, subtraction, division and multiplication operations.

The amount of gas Karen has can be found using basic arithmetic operations as follows;

On Monday, Karen needed to put 5 gallons 3 quarts of gas into her boat. Since 1 gallon is equal to 4 quarts, this is equivalent to (5 × 4 + 3) = 23 quarts of gas

On Saturday, she needed to put twice as much gas into her boat as she did on Monday. So on Saturday she needed to put (2 × 23) = 46 quarts of gas into her boat.

Since, Karen had 18 gallon jug of gas available and 1 gallon is equal to 4 quarts, this mean she had (18 × 4) = 72 quarts of gas available.

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Using Geometric Mean Theorem, In the given triangle, The length of altitude is 12.

The geometric mean theorem states that in a right triangle, the length of the altitude from the right angle to the hypotenuse is the geometric mean of the lengths of the two segments of the hypotenuse

In other words, the square of the length of the altitude from the right angle to the hypotenuse is equal to the product of the lengths of the two segments of the hypotenuse. And the length of the altitude itself is equal to the square root of this product.

Now,

As we know

using Geometric Mean Theorem,

hypotenuse=18+8=26

let base=a

then   26/a=a/8

a²=208

Now, using Pythagoras theorem

8²+(x+9)²=a²

(x+9)²=208-64

x+9=√144

x+9=12

Hence, The length of altitude is 12.

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By answering the presented question, we may conclude that

a) both tanks will have the same amount of water after 20 minutes.

b) difference in time required to thoroughly drain them is: 60 - 44 = 16 minutes.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

Part A:

Let's assume that after t minutes, the amount of water remaining in tank A is x gallons, and the amount of water remaining in tank B is also x gallons. We can write equations based on the given information:

Tank A: x = 220 - 5t

Tank B: x = 180 - 3t

To find the time when both tanks have the same amount of water, we can set these two equations equal to each other and solve for t:

220 - 5t = 180 - 3t

40 = 2t

t = 20

Therefore, both tanks will have the same amount of water after 20 minutes.

Part B:

To determine which tank will be completely drained first, we need to find the time it takes for each tank to be completely drained. For tank A, we can set x = 0 in the equation we found in part A:

0 = 220 - 5t

t = 44

So it will take 44 minutes for tank A to be completely drained.

For tank B, we can set x = 0 in the equation given in the problem:

0 = 180 - 3t

t = 60

So it will take 60 minutes for tank B to be completely drained.

Therefore, tank A will be completely drained first. The amount of time it takes for tank A to be completely drained is 44 minutes, and the amount of time it takes for tank B to be completely drained is 60 minutes. The difference in time is:

60 - 44 = 16 minutes.

The difference in time required to thoroughly drain them is: 60 - 44 = 16 minutes.

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The altitude of drone is 8.4ft.

The angle generates in between the horizontal line and the line of sight when an observer looks upward is referred to as the angle of elevation in mathematics. It is always greater than the observer and at a larger angle.

The term "angle of depression" defined as the angle created when an observer looks down at an item and the horizontal line intersects with the line of sight. It gauges how our area of vision shifts as we see down.

In the given figure,

∠DTL=35°

LT=12ft

tan35°=DL/LT

tan35°=DL/12

DL=8.4ft

Hence, The altitude of drone is 8.4ft.

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False to say that "cos(0) = 0." Cos(0) is equal to 1, as the input yields the x-coordinate of the spot on the circle for each arc in right spot, where first side coincides positive x-axis or final side spins clockwise first side.

What does it mean to coincide?

occupying the same location in time or space; coinciding; taking up the same spots on a scale. 3. Exactly concur.

Nevertheless, if the query is changed to ask for the angle that measures between 0 & 2 radians for which cos(x) = 0, the response is:

When x is equal to 2 or 3, cos(x) equals 0. The unit circle's corresponding points at these angles are, respectively, (0, 1) and (0, -1).

b. The sin(x) values for these angle measurements are:

As the equivalent point is at (0, 1) just on unit circle, sin(/2) equals 1.Due to (0, -1) being the corresponding point on the unit circle, sin(3/2) = -1.

therefore, False to say that "cos(0) = 0." Cos(0) is equal to 1, as the input yields the x-coordinate of the spot on the circle for each arc in right spot, where first side coincides positive x-axis or final side spins clockwise first side.

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