What is the value of k in the equation below?

5 k minus 2 k = 12

Answer:

11.2

Step-by-step explanation:

multiply 1.6 by 7 since that's how many days there are in a week

Answer:

11.2

Step-by-step explanation:

you collect 1.6 packs of chile peppers a day there is 7 days in a week 1.6x7=11.2

hope it helps.

The logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

The exponential function in this problem is defined as follows:

8e^x-5 = 0.

The equation can be sorted isolating the exponential as follows:

8e^x = 5.

e^x = 5/8.

The natural logarithm(symbolized by the ln) is the opposite of the exponential function, hence the logarithmic form of the equation is presented as follows:

ln(e^x) = ln(5/8).

As stated above, the natural logarithm and the exponential functions are inverse functions, meaning that:

ln(e^x) = x.

Thus the logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

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Answer:

1.17 , 1.7 , 7.117 , 7.13 , 7.2

this is the arranged order

The hypothesis test is left-tailed because the financial analyst wants to test if the proportion of stock portfolios containing high-risk stocks is lower than 0.10.

In other words, they are interested in determining if the proportion is significantly less than the specified value of 0.10. A left-tailed hypothesis test is used when the alternative hypothesis suggests that the parameter of interest is smaller than the hypothesized value. In this case, the alternative hypothesis would be that the proportion of stock portfolios with high-risk stocks is less than 0.10.

By conducting a left-tailed test, the financial analyst is trying to gather evidence to support their claim that their clients have a lower proportion of high-risk stock portfolios. They want to determine if the observed data provides sufficient evidence to conclude that the true proportion is indeed less than 0.10, which would support their claim of a lower proportion of high-risk stocks.

Therefore, a left-tailed hypothesis test is appropriate in this scenario.

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Answer:

b. $9.96

Step-by-step explanation:

To solve this problem, let's first calculate how much Nina charges for shipping per painting. We'll divide the total shipping cost by the number of paintings sold.

When Nina sells 4 paintings and charges a total of $9.96 for shipping:

Shipping cost per painting = $9.96 / 4 = $2.49

When Nina sells 8 paintings and charges a total of $19.92 for shipping:

Shipping cost per painting = $19.92 / 8 = $2.49

We can see that regardless of the number of paintings sold, Nina charges $2.49 for shipping per painting.

Now let's calculate how much Nina charges for shipping 20 paintings and 16 paintings:

Shipping cost for 20 paintings = $2.49 * 20 = $49.80

Shipping cost for 16 paintings = $2.49 * 16 = $39.84

The difference in shipping charges for 20 paintings and 16 paintings is:

$49.80 - $39.84 = $9.96

Therefore, Nina charges $9.96 more for shipping 20 paintings than for shipping 16 paintings. The correct option is (b) $9.96.

ANSWER and EXPLANATION

a) To simplify the radical, we have to:

1) First, express the number inside the radical as a product of a perfect square and a number that is not a perfect square.

2) Next, we separate the numbers into two radicals and find the square root of the perfect square.

3) Finally, we find the product of the number and the remaining radical.

B) Following the steps above:

STEP 1

STEP 2

STEP 3

Step-by-step explanation:

= -2(x - 5) + 4(9 + x)

= -2x + 10 + 36 + 4x

= (-2 + 4)x + 10 + 36

= 2x + 46

Answer:

180 - 55 = angle 1

80 - 55 = 25 so 180 - 55 = 125

angle 1 = 125 degrees

The equation is: G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the graph, we see that:

y-intercept = 15 gallons

Now, the slope is gotten from the formula:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (10 - 5)/(4 - 8)

Slope = -⁵/₄

Thus, equation is:

G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

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Answer:

-7//40

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

5 + 7 = 12

8 + 7 = 15

12/15 simplified into 4/5

Answer:

Option C

Step-by-step explanation:

you cancel the whole parentheses.

So you know, x+6 can't equal to 0.

that's why there is a choice that is all real numbers but not -6.

Answer:

A. All real numbers

Step-by-step explanation:

Given

On cross multiplying,

Answer:

Beginning at the x-coordinate, move vertically, the direction of the y-axis, the distance given by the y-coordinate. If the y-coordinate is positive, move up; if the y-coordinate is negative, move down.

Step-by-step explanation:

Answer:

well which direction?

Step-by-step explanation:

Step-by-step explanation:

is 0 I think I don't know maybe

Answer:

Step-by-step explanation:

The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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The proper order of the designs, from the one with the least amount of control over variables to the most, is (b) one-group pretest posttest, quasi-experimental, pretest posttest control group, Solomon four-group.

The designs can be ordered based on the level of control they provide over variables. The one-group pretest posttest design (b) has the least amount of control as it lacks a control group. The quasi-experimental design (d) provides some control but still lacks random assignment. The pretest posttest control group design (c) includes a control group but lacks random assignment of participants. Finally, the Solomon four-group design (a) provides the highest level of control as it includes both a pretest posttest control group design and a quasi-experimental design, allowing for comparisons and additional control.

By considering the features of each design, we can determine the level of control they offer over variables. It's important to note that the proper order may vary depending on the specific research context and the researcher's goals.

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Using linear approximation, the estimated distance the boat will coast is approximately 266 feet. (Rounded to the nearest whole number.)

To estimate the distance the boat will coast using a linear approximation, we can consider the average velocity over the given time interval.

The initial velocity is 39 ft/s, and 9 seconds later, the velocity decreases to 20 ft/s. Thus, the average velocity can be approximated as:

Average velocity = (39 ft/s + 20 ft/s) / 2 = 29.5 ft/s

To estimate the distance traveled, we can multiply the average velocity by the time interval of 9 seconds:

Distance ≈ Average velocity * Time interval = 29.5 ft/s * 9 s ≈ 265.5 ft

Using linear approximation, we estimate that the boat will coast approximately 266 feet.

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The correct answer is:

0.025 P-value < 0.05

In statistical hypothesis testing, the P-value is a measure of the strength of evidence against the null hypothesis. It represents the probability of observing a test statistic as extreme as the one calculated from the sample data, assuming the null hypothesis is true.

In this case, we have a right-tailed test, which means we are interested in the upper tail of the F-distribution. The test statistic is calculated as F = 2.97, with degrees of freedom for the numerator (d.f.N.) = 9 and degrees of freedom for the denominator (d.f.D.) = 14.

Using Table H (which provides critical values for the F-distribution), we can determine the P-value interval. In this table, we find the column for d.f.N. = 9 and locate the row that corresponds to d.f.D. = 14. The intersection of these values gives us the critical value, which is 0.025.

Since the F-value of 2.97 is greater than the critical value of 0.025, the P-value is less than 0.05. Therefore, we can conclude that 0.025 < P-value < 0.05, indicating strong evidence against the null hypothesis.

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Therefore, the square root of the given number \(\sqrt1444 = 38.\)

The square root of a number is a value that, when multiplied by itself, gives the original number.

When we talk about the square root of a number, we're looking for a quantity that, when multiplied by itself, equals the original number. It's like asking, "what number of times itself gives me this number?" In your case, the number is 1444.

The mathematical symbol for square root is √. So, when we write √1444, we're asking, "what number times itself gives me 1444?"

Through mathematical calculation or reference tables, we find that 38*38 equals 1444.

In the case of 1444, the square root is 38.

This is because 38*38 equals 1444.

Therefore, \(\sqrt1444 = 38.\)

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Answer: 4

Step-by-step explanation: If Caleb starts with 4 and subtracts 6, he'll get -2. -2 times 2, equals -4. If he starts with 4 and subtracts 8, he'll again end up with -4, meaning the original number is 4!

4-6= (-2)

-2*2= (-4)

4-8= (-4)

Document 1 and Document 2 are more similar based on the vector space model representation, Euclidean distance, and cosine distance calculations.

(a) Representing the documents as 5-dimensional vectors:

To represent the documents as 5-dimensional vectors, we will use the provided dictionary terms and assign a binary value indicating the presence (1) or absence (0) of each term in a document.

Document 1: [1, 1, 1, 1, 0]

Document 2: [0, 1, 1, 1, 1]

Document 3: [0, 0, 1, 0, 1]

In the vector representation, each dimension corresponds to a term in the dictionary.

(b) Calculating Euclidean and cosine distances:

Euclidean distance measures the straight-line distance between two points in the vector space. Cosine distance measures the angle between two vectors.

Euclidean distance between Document 1 and Document 2:

√((1-0)^2 + (1-1)^2 + (1-1)^2 + (1-1)^2 + (0-1)^2) = √(1) = 1

Cosine distance between Document 1 and Document 2:

(10 + 11 + 11 + 11 + 0*1) / (√(1+1+1+1) * √(0+1+1+1+1)) = 3 / (2 * 2) = 0.75

Euclidean distance between Document 1 and Document 3:

√((1-0)^2 + (1-0)^2 + (1-1)^2 + (1-0)^2 + (0-1)^2) = √(2) ≈ 1.414

Cosine distance between Document 1 and Document 3:

(10 + 10 + 11 + 10 + 0*1) / (√(1+1+1+1) * √(0+0+1+0+1)) = 1 / (2 * √2) ≈ 0.354

Euclidean distance between Document 2 and Document 3:

√((0-0)^2 + (1-0)^2 + (1-1)^2 + (1-0)^2 + (1-1)^2) = √(2) ≈ 1.414

Cosine distance between Document 2 and Document 3:

(00 + 10 + 11 + 10 + 1*1) / (√(0+1+1+1+1) * √(0+0+1+0+1)) = 2 / (2 * √2) ≈ 0.707

(c) Constructing the distance matrix:

The distance matrix represents the distances between each pair of vectors.

Doc 1 | 0 | 1 |1.414 |

Doc 2 | 1 | 0 |1.414 |

Doc 3 |1.414 |1.414 | 0 |

(d) Determining the most similar pair of documents:

Based on the distance matrix, we can observe that Document 1 and Document 2 have the smallest distances in both Euclidean and cosine distances. Therefore, Document 1 and Document 2 are more similar to each other compared to the other document pairs.

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It would take Jenna half an hour, or 30 minutes, to run 3 km.

Hope this helps!

Answer:

x = 1/2y + 3/2

y = 2x - 3

Step-by-step explanation:

The rectangle with the maximum area, formed by its base on the x-axis and two vertices on the parabola y = 49 - x^2, has dimensions of length 14 units and height 0 units.

To find the dimensions of the rectangle that maximize its area, we need to consider the relationship between the rectangle's dimensions and the parabola.

Let's assume the length of the rectangle is 2x, and the height is y. Since the base of the rectangle lies on the x-axis, the y-coordinate of the two vertices on the parabola will be zero.

Substituting the y-coordinate into the equation of the parabola, we have:

0 = 49 - x^2

Rearranging the equation:

x^2 = 49

Taking the square root of both sides:

x = ±√49

Since we are interested in the positive value of x, we have:

x = 7

Now, substituting this value back into the equation of the parabola, we can find the height:

y = 49 - (7^2)

y = 0

Therefore, the dimensions of the rectangle that maximize its area are:

Length = 2x = 2 * 7 = 14 units

Height = y = 0 units

The rectangle is a degenerate rectangle, which means it has a height of zero. In this case, the maximum area is achieved when the rectangle becomes a line segment on the x-axis with a length of 14 units.

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The given question is incomplete, the complete question is,

What are the dimensions of the rectangle that can be constructed with its base on the x-axis and two vertices on the parabola y = 49 - x^2, in order to maximize its area?

The area of the track will be 78501 m². The area of the track is equal to the area of the circle.

The space filled by a flat form or the surface of an item is known as the area.

The number of unit squares that cover the surface of a closed-form is the figure's area. Square meters and other similar units are used to measure area.

The area of the track is found as;

\(\rm A=\frac{\pi}{4} d^2 \\\\ \rm A=\frac{3.14}{4} (100)^2 \\\\ A=7850 \ m^2\)

Hence, the area of the track will be 78501 m².

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Answer:

1. Combining like terms

2. Distributive property

3. Subtraction (both sides)

4. Addition(both sides)

5. Division

Step-by-step explanation:

1. Colinear points are the ones that are in the same line.

In this example, K is colinear to J and L (referring to line a).

It can be N and M, referring to line c.

2. As the line has the points H and K included, it can be named HK.

3. The intersection of a line and a plane, assuming that the line is not included in the plane, is a point. In this case, the intersection of line c and plane R is point K.

4. A point is coplanar to a plane or another point when it belongs to the plane.

In this case the point M is not coplanar to the plane R (it is outside of the plane).

5. Each face of the prism is a plane and it is can be defined by 3 points. So in this case we have 5 planes (four faces and one base, that is W).

6. We can assign a name for a plane with 3 points that belong to that plane. A possible name is ABC.

7. The intersection of plane W and ADE is the line that goes through the points A and D. We can call this line with the name AD.

8. E, C or D are no colinear to A and B. They do not belong to the line that goes through the points A and B (or the line AB).

9. DF is the sum of DE and EF, so we have:

DE = 29

10. We know that:

11. If S is the midpoint of RT, then RS=ST.

We would have:

12. If y bisects AC, then AB=BC. Then we have:

13. AB is half the value of AC, so we have:

Then, we can calculate CD = AC

We can define DE as DE = CE - CD. We can calculate it as:

DE = 11

The real output will decrease by less than $600 billion and the price level will fall if Aggregate Demand (AD) moves to the left by $600 billion and aggregate Supply moves upward.

It is generally accepted that supply tends to rise: as the cost rises, providers will deliver more. The request is by and large considered to incline to descend: Customers make fewer purchases at higher prices.

An increase in aggregate demand will cause prices to rise and output to rise if aggregate supply slopes upward. The planned inventory rises above the desired level when aggregate demand is lower than aggregate supply.

To clear the undesirable expansion in stock, firms intend to diminish the creation yield till Total interest becomes equivalent to Total stock.

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