Prove by cases that 25k^2 + 15k is an even integer whenever 5k- 3 is an integer. ​

The data in the table of values can be used to find the line of best fit after plotting the graph

a. Please find attached the graph of the data showing the next two points on the table, which are (9, 9.8), (7, 11)

b. Linear correlation

c. Please find attached the graph of the data showing the line of best fit created with MS Excel

A line of best fit is a line that passes through a set of scatter plot, which most precisely reflects the relationship between the points.

a. Please find attached the graph of the data in the table, including the plot of the next two points (9, 9.8), and (7, 11), created with MS Excel

b. The type of correlation on the graph which consists of a straight line that is drawn across the points such that the distance between the line and the points on the graph is minimized, is a linear correlation.

c) The line of best fit, can be obtained adding the Trendline chart element on MS Excel, which can be obtained as follows;

Please find attached the graph of the Number of hours sleep to the Age of the children, showing the line of best fit, created with MS Excel

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To evaluate the series Σ(3^n/(141·3²ⁿ) from n=1 to infinity converges or diverges, we can use the ratio test.

The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges absolutely;

if the limit is greater than 1, then the series diverges; and if the limit is exactly 1, then the test is inconclusive.

Let's first apply the ratio test to this series:

| (3ⁿ+¹/(141·3²ⁿ+¹) * (141·3²ⁿ))/(3ⁿ |

= | 3/141 |

= 1/47

Since the limit of the absolute value of the ratio of consecutive terms is less than 1, the series converges absolutely.

To compute the sum of the series, we can use the formula for the sum of a geometric series:

Σ(3ⁿ/(141·3²ⁿ) = 3/141 Σ(1/9)ⁿ from n=1 to infinity

= (3/141) · (1/(1-(1/9)))

= 27/470

Therefore, the series converges absolutely and its sum is 27/470.

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The number of portion with each having 12 fruits is at most 6 portions.

To divide the fruits into 12 portions

Total number of fruits = 80

Number of fruits per portion = 12

Number of fruits per portion = (Total number of fruits / Number of fruits per portion )

Number of fruits per portion = 80/12 = 6.67

Therefore, to divide the fruits into 12 fruits , There would be at most 6 portions.

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Answer: -5/3

Step-by-step explanation:

Answer: m = -4/3

Step-by-step explanation:

If you're given two different coordinates, and you want to find the slope, the general rule is that you subtract the first coordinates from the first. The formula for these kinds of problems is \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) .

Answer:

35.6 minutes

Step-by-step explanation:

The average (aka mean) of a set of values is defined as the sum of the values divided by the total number of values.

Step 1:  Find sum of values:

According to the dot plot: person talked 0 minutes

Now we can find the sum using addition and multiplication:

Sum = (1 * 0) + (2 * 10) + (2 * 20) + (4 * 30) + (3 * 50) + (4 * 60)

Sum = 0 + 20 + 40 + 120 + 150 + 240

Sum = 570

Step 2:  Find the total number of values present.

To find the total number of values, we add up the total number of people present:

Total = 1 + 2 + 2 + 4 + 3 + 4

Total = 16

Step 3:  Determine average by dividing sum of values by total number of values.  Then round to the nearest tenth:

Average = 570 / 16

Average = 35.625

Average = 35.6

Thus, the average number of minutes spent talking on a cell phone was about 35.6 minutes

The equation of the plane that passes through the point (8,13,4) and is parallel to the plane x+y+z=3 is 7x + 6y - z = 77.

To find the equation of a plane parallel to a given plane, we can use the fact that parallel planes have the same normal vector. The normal vector of the plane x+y+z=3 is (1,1,1), as the coefficients of x, y, and z represent the direction perpendicular to the plane.

We know that the desired plane passes through the point (8,13,4), so we can use this point along with the normal vector to form the equation of the plane using the point-normal form.

Using the point-normal form, the equation of the plane is given by:

(x - 8, y - 13, z - 4) · (1,1,1) = 0

(x - 8) + (y - 13) + (z - 4) = 0

x + y + z = 25

However, we want a plane parallel to the given plane x+y+z=3, so we can multiply the equation by a constant to obtain a parallel plane. In this case, we can multiply each term by 7 to get:

7x + 7y + 7z = 175

Finally, we can simplify the equation to get the desired form:

7x + 6y - z = 77

Therefore, the equation of the plane that passes through (8,13,4) and is parallel to x+y+z=3 is 7x + 6y - z = 77.

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Answer:

4/5

Step-by-step explanation:

because 1/5 + 4/5 = 1

Answer:

the answer is 6C4 (2x)2 (-Y2)4

Step-by-step explanation:

Answer:

the second answer is D

Step-by-step explanation:

on edge

Answer:

27%

Step-by-step explanation:

The name of every month ends in the letter y is the given statement. February is a counterexample to this statement. This is because February does not end with the letter 'y'. So the right  option is (c) February.

What is a counterexample?

In mathematics, a counterexample is an example that opposes or disproves a statement, proposition, or theorem. It is a scenario, an instance, or an example that goes against the given statement.

Therefore, a counterexample demonstrates that the given statement is false or invalid.In this case, the statement is: "The name of every month ends in the letter y." We have to find which of the months listed does not end in "y."February is the only month in the options listed that does not end in the letter "y."

Thus, it is a counterexample to the given statement. Therefore, the correct option is C, February.

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Answer:

x= 4 and y= 2

Step-by-step explanation:

3x+3y= 18 (1)

2y= x (2)

from (1):

x+y= 6

y= 6-x (3)

sub (3) into (2):

2(6-x)= x

12-2x= x

-3x= -12

x= 4 (4)

sub (4) into (3):

y= 6-4

= 2

An electric circuit is a closed course that consists of all of the additives linked to finish the go with the drift of modern-day.

The circuit underneath is composed of:

A battery as a supply of direct modern-day which materials electricity within side the circuit for modern-day to go with the drift. Direct modern-day affords uni-directional modern-day. Here it has cells. Here 4 cells are linked in collection for the battery.

Two bulbs A and B linked in parallel connection. Each bulb has been parallel connected with a voltmeter.

A voltmeter measures the voltage throughout the element that it's miles linked with. It is continually linked in parallel with the additives.

Main circuit has an ammeter in collection with the battery and connection of bulb.

An ammeter measures the modern-day flowing within side the circuit. It is continually linked in collection.

Therefore, an electric circuit is a closed course that consists of all of the additives linked to finish the go with the drift of modern-day.

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The perimeter of the isosceles right triangle is P = 6 + 3√2 feet

A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.

In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle

The three types of Isosceles Triangles are :

Isosceles acute triangle

Isosceles right triangle

Isosceles obtuse triangle

Given data ,

Let the isosceles triangle be represented as ΔABC

In an isosceles right triangle, the two legs are congruent, so if one leg has a length of 3 ft, then the other leg also has a length of 3 ft. Let's call the length of the hypotenuse h.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

h² = 3² + 3²

h² = 18

Taking square roots on both sides , we get

h = 3√2 feet

The perimeter of the triangle is the sum of the lengths of its sides:

Perimeter = 3 + 3 + 3√2 = 6 + 6 + 3√2 feet

Hence , the perimeter is 6 + 3√2 feet

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a. Measurement Model for the Repeated Addition Approach: 3 × 4

To illustrate the Measurement Model for the Repeated Addition Approach, we can use the example of 3 × 4.

Step 1: Draw three rows and four columns to represent the groups and the items within each group.

|  |  |  |  |

|  |  |  |  |

|  |  |  |  |

Step 2: Fill each box with a dot or a small shape to represent the items.

|● |● |● |● |

|● |● |● |● |

|● |● |● |● |

Step 3: Count the total number of dots to find the product.

In this case, there are 12 dots, so 3 × 4 = 12.

b. Set Model for the Repeated Addition Approach: 4 × 3

To illustrate the Set Model for the Repeated Addition Approach, we can use the example of 4 × 3.

Step 1: Draw four circles or sets to represent the groups.

●

●

●

●

Step 2: Place three items in each set.

●  ●  ●

●  ●  ●

●  ●  ●

●  ●  ●

Step 3: Count the total number of items to find the product.

In this case, there are 12 items, so 4 × 3 = 12.

c. The property of whole number multiplication illustrated by the problems in parts a and b is the commutative property.

The commutative property of multiplication states that the order of the factors does not affect the product. In both parts a and b, we have one multiplication problem written as 3 × 4 and another written as 4 × 3.

The product is the same in both cases (12), regardless of the order of the factors. This demonstrates the commutative property of multiplication.

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As given, the 99% confidence interval is (-0.13, 0.37).

To check if the coffee shop owner's claim is justified, we can check if the confidence interval contains zero. If it does, then we cannot reject the null hypothesis (the claim), and if it doesn't, then we reject the null hypothesis.

In this case, the interval (-0.13, 0.37) contains zero, hence we cannot reject the null hypothesis at a 99% level of confidence. Therefore, we can say that there is not enough evidence to support the owner's claim that customers who drink espresso are less likely to use their own cup compared with customers who drink coffee.

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The binary representation is (a) a3 in binary is 10100011(b) 1fc in binary is 11111100(c) 2a0b in binary is 1010100000001011

In hexadecimal, each digit represents four bits, which means that two hexadecimal digits can represent eight bits. As a result, converting from hexadecimal to binary is straightforward. The four bits corresponding to each hexadecimal digit can be written down, resulting in an 8-bit binary value.

To convert hexadecimal to binary, simply convert each hexadecimal digit to binary, then combine them to get the final binary representation. For instance, in a, the hexadecimal digit a has a binary representation of 1010, while the digit 3 has a binary representation of 0011.

Combining these results in a binary representation of 10100011. Similarly, the binary representations of 1f and c are 00011111 and 00001100, respectively.

Combining them results in 11111100. Finally, the binary representation of 2a0b is obtained by converting 2, a, 0, and b to binary, resulting in 0010, 1010, 0000, and 1011, respectively. Combining them results in 1010100000001011.

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5 is the missing value of x.

From the intersecting of two chords theorem,

Given angle= 14x-1

Arcs are 13x+8, 65°

From the theorem,

14x-1 = (13x+8 + 65)/2

14x-1 = (13x+73)/2

28x-2=13x+73

15x=75

x= 5

Therefore, the value of x will be 5 for the given figure.

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Answer:

32 times

Step-by-step explanation:

1/8 x 8= 1

1/8 x 32= 4

Answer:

Mike should use 32 times this teaspoon to measure 4 teaspoons of vanilla extract.

Step-by-step explanation:

1/8x=4

x=4/(1/8)=(4/1)(8/1)=32/1=32

50% οr less οf qualifying incοme, at least twο credit references fοr each bοrrοwer withοut a credit scοre.

The number οf nοn-traditiοnal credit references required fοr a bοrrοwer with nο credit scοre can vary depending οn the lender and their specific requirements. Generally, lenders may ask fοr alternative credit references tο assess the bοrrοwer's creditwοrthiness in the absence οf a traditiοnal credit scοre. These alternative references cοuld include:

Rental payment histοry: Prοviding evidence οf οn-time rental payments and a gοοd rental histοry can serve as a pοsitive credit reference.

Utility bills: Shοwing cοnsistent and timely payment οf utility bills such as electricity, water, οr gas can demοnstrate respοnsible financial behaviοr.

Cell phοne bills: Submitting prοοf οf regular and timely payments fοr cell phοne bills can be cοnsidered as a credit reference.

Bank statements: Prοviding bank statements that shοw regular depοsits, savings, and respοnsible mοney management can be used as a credit reference.

Emplοyment histοry: Demοnstrating a stable emplοyment histοry and prοviding emplοyment verificatiοn can be cοnsidered as a nοn-traditiοnal credit reference.

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Complete question:

How many non traditional credit references are required for a borrower with no credit score?

The total surface area of a cylinder is 351.68 square meter.

The surface area of a cylinder refers to the total area that the cylinder's curved surface and circular bases cover. The total surface area of the cylinder includes the area of the 2 bases of the cylinder (each of which is in the shape of a circle) and the area of the curved surface.

We know that, the total surface area of a cylinder is 2πr(r + h).

From the given figure, radius of a cylinder is 8/2 = 4 m and height is 10 m.

Here, total surface area = 2×3.14×4(4+10)

= 25.12×14

= 351.68 square meter

Therefore, the total surface area of a cylinder is 351.68 square meter.

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answer is 142

hope that helped

Answer:

m<1 = 180

Step-by-step explanation:

hope this helps sorry if incorrect have a good rest of your afternoon :) ❤

Part A: An open circle on a number line represents an excluded value, indicating that the endpoint is not included in the solution set of the inequality. It is used when the inequality includes the symbols < (less than) or > (greater than), which denote strict inequality.

Part B: A closed circle on a number line represents an included value, indicating that the endpoint is part of the solution set of the inequality. It is used when the inequality includes the symbols ≤ (less than or equal to) or ≥ (greater than or equal to), which denote inclusive inequality.

Part C: The shading on the number line represents the range of values that satisfy the given inequality. It indicates which values make the inequality true. Typically, the shading is done to the right or left of the circle(s) depending on whether the inequality is greater than or less than.

Part A:

For example, if we have the inequality x > 2, we would represent it with an open circle at 2 on the number line. This means that 2 itself is not a valid solution, but any value greater than 2 is included.

Part B:

For example, if we have the inequality x ≥ -3, we would represent it with a closed circle at -3 on the number line. This means that -3 itself is a valid solution, as well as any value greater than or equal to -3.

Part C:

For example, if we have the inequality x > 2, we would shade the portion of the number line to the right of the open circle at 2. The shaded region represents all the values greater than 2 that satisfy the inequality. The shading visually illustrates the solution set and helps identify the range of valid values for the variable in the given inequality.

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Answer: UNDEFINED

Step-by-step explanation:

x=-5y+4      5y=-x+4       y=-1/5x+4/5

3x+15y= -1    15y=-3x-1    y=-1/5x-1/15

COMBINED: -1/5x+4/5=-1/5x-1/15 FIND COMMON DENOMINATOR=15

-3/15x=-3/15x-13/15

0=-13/15    UNDEFINED

The probability of getting an odd number or a divisor of 9 when spinning the spinner once is 75%

To calculate the probability of getting an odd number or a divisor of 9 when spinning the spinner once, we need to first identify the possible outcomes.

The spinner can have 8 possible outcomes, which are: 1, 2, 3, 4, 5, 6, 9, and 10. Out of these outcomes, we have 4 odd numbers (1, 3, 5, and 9) and 2 divisors of 9 (9 and 10).

To calculate the probability, we need to add the probabilities of getting an odd number and a divisor of 9, and then subtract the probability of getting both an odd number and a divisor of 9 (since that would be counted twice otherwise).

P(odd or divisor of 9) = P(odd) + P(divisor of 9) - P(odd and divisor of 9)

P(odd) = 4/8 = 1/2

P(divisor of 9) = 2/8 = 1/4

P(odd and divisor of 9) = 0 (there is no number that is both odd and a divisor of 9)

Substituting the values, we get:

P(odd or divisor of 9) = 1/2 + 1/4 - 0 = 3/4

To convert this into a percentage, we multiply by 100:

P(odd or divisor of 9) = 75%

Therefore, the probability of getting an odd number or a divisor of 9 when spinning the spinner once is 75%.

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The formula for finding (66 + 78) using the greatest common factor, GCF, and the distributive property is 6(11+13).

For the stated question-

Evaluating the total of 66 + 78.

The GCF as well as the distributive property, however, are mentioned in the question as being employed in this assessment.

Because the GCF of 66 and 78 is 6, this means that.

Thus, we can infer that 6(11+13) is the necessary expression.

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The linear speed is 141.37ft/min.

The relation between the linear speed v and rotational speed (ω) is given by the relation

v=rω.

we know that rotational speed is the speed with which we measure rotations. So

ω=Number of Rotations/Time in minutes.

linear speed:

v=2πrn/T

Linear speed is defined as the wheel would have traveled, had it been rolling on a flat surface.

The given information is the revolution speed of the Ferris wheel as 1 revolution in 8 min.

we can observe that if the wheel rotates one full revolution, the distance that it covers is equal to the circumference of the wheel. In one revolution the distance it travels is

2*π*(180)

distance=1130.9733 ft.

Also, it takes 8 min to complete the distance. so the linear speed is

speed=distance/time

=1130.9733/8

speed=141.37 ft/min.

Hence, the linear speed of the Ferris wheel is 141.37 ft/min.

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Answer:

40 units^2

Step-by-step explanation: