What is the nth term rule of the quadratic sequence below?
8
,
14
,
22
,
32
,
44
,
58
,
74
,
.
.
.

Options (a) and (b) have smaller absolute values of the correlation coefficient, indicating weaker linear relationships. Option (d) is incorrect as the correlation coefficient measures the linear relationship between two variables, which would be represented as a straight line on a scatter plot.

The Pearson correlation measures the strength and direction of the linear relationship between two variables. A correlation coefficient of -1 indicates a perfect negative linear relationship, a correlation coefficient of 0 indicates no linear relationship, and a correlation coefficient of +1 indicates a perfect positive linear relationship.

In general, the closer the absolute value of the correlation coefficient is to 1, the closer the data points will be to a straight line. Therefore, among the given options, the correlation coefficient that would result in data points being clustered most closely around a straight line is option (c) r = –0.70, which indicates a strong negative linear relationship between the two variables. When the correlation is close to -1, the data points tend to form a straight line with a negative slope, indicating a strong and consistent negative relationship between the two variables.

Options (a) and (b) have smaller absolute values of the correlation coefficient, indicating weaker linear relationships. Option (d) is incorrect as the correlation coefficient measures the linear relationship between two variables, which would be represented as a straight line on a scatter plot.

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The conversion of a fraction number with denominator 5 and numerator 2 , 2/5 in decimals is equals to the 0.4 value.

A decimal number can be defined as a number whose whole number part and fractional part are separated by a decimal point. Writing 2/5 as a decimal number by converting the denominator to powers of 10. We multiply the numerator and denominator by a number so that the denominator is a power of 10.

2/5 = (2 × 2) / (5 × 2) = 4/10

Now move the decimal point to the left as many places as there are zeros in the denominator, which is a power of 10.

The decimal moved one place to the left because the denominator was 10. Therefore, 4/10 = 0.4. Hence, required value is 0.4.

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The space inside the cylinder but outside the inscribed cone has a volume of 36π cubic centimeters.

Let's assume the radius of the cone is r and the height is h. Since the cone is inscribed in the cylinder, the base radius of the cone is equal to the radius of the cylinder, and the height of the cone is equal to the height of the cylinder.

The volume of a cylinder is given by V_cylinder = π\(r^2\)h, and in this case, we are given that the volume of the cylinder is 72π cubic centimeters.

72π = π\(r^2\)h

Simplifying the equation, we have:

\(r^2\)h = 72

Now, the volume of a cone is given by V_cone = (1/3)π\(r^2\)h. Since the cone is inscribed in the cylinder, its base radius and height are the same as that of the cylinder.

The volume of the space inside the cylinder but outside the cone is the difference between the volume of the cylinder and the volume of the cone:

V_space = V_cylinder - V_cone

Substituting the values, we have:

V_space = π\(r^2\)h - (1/3)π\(r^2\)h

Simplifying further, we get:

V_space = (2/3)π\(r^2\)h

Since \(r^2\)h = 72 from the earlier equation, we can substitute this value:

V_space = (2/3)π(72)

V_space = 48π

Therefore, the space inside the cylinder but outside the cone has a volume of 48π cubic centimeters, or 36π cubic centimeters after simplification.

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Answer:

52 hours and 25 min

Step-by-step explanation:

2 1/2+45+4.75= 52.25

Answer:

6 cups of flour

Step-by-step explanation:

we know that

the ratio of the recipe=(1 1/2)/(3/4)

1 1/2=1.5 cups of flour

3/4 stick of butter-------> 0.75 stick of butter

by proportion

1.5/0.75=x/3---------> 3*1.5=0.75*x

x=3*1.5/0.75----------> x=6 cups of flour

Answer:

$123.89

Step-by-step explanation:

51.88 + 72.01 = 123.89

Answer:

123.89

Step-by-step explanation:

$51.88 + $72.01= 123.89:)

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Answer:

x = 0.5

Step-by-step explanation:

The result can be shown in multiple forms. This one is decimal form.

Answer:

The answer is

\(x = 12 \\ y = 20 \\ z = 15\)

Step-by-step explanation:

By using Pythagoras low

Then we can find that

\( {y}^{2} = {x}^{2} + {16}^{2} \\ {z}^{2} = {x}^{2} + {9}^{2} \\ {y}^{2} + {z}^{2} = {25}^{2} \\ then \\ {x}^{2} + {9}^{2} + {x}^{2} + {16}^{2} = {25}^{2} \\ 2 {x}^{2} = 288 \\ x = 12 \\ By \: substituting \: x \: into \: the \: previous \: equations \\ then \: \\ y = 20 \\ z = 15\)

Answer:

The answer is

Step-by-step explanation:

By using Pythagoras low

Then we can find that

Step-by-step explanation:

The correct simplification of the expression is c12 (option c).

The expression (c^4)^3 can be simplified using the exponent rules for powers of a power, which states that when a power is raised to another power, we can multiply the exponents.

Thus, we have:

(c^4)^3 = c^(43) [Using the rule (a^m)^n = a^(mn)]

Simplifying the exponent 4*3, we get:

c^(4*3) = c^12

Therefore, the correct simplification of the expression is c^12.

Option (c) is the correct answer as it correctly represents the simplified form of the given expression. Option (a) c^-1, option (b) c^7, and option (d) c^64 are not correct because they do not follow the exponent rules used to simplify the expression.

In summary, the expression (c^4)^3 simplifies to c^12, which is option (c) in the given options.

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Que knows that the required hypotenuse of the given right triangle is 18.35 units from the Pythagorean theorem.

To determine the undiscovered side of a right-angled triangle, utilize the Pythagoras theorem.

The hypotenuse (third side) of a right-angled triangle, for instance, can be determined using the formula c2 = a2 + b2, where 'c' stands for the hypotenuse and 'a' and 'b' are the two legs.

So, we have:

Height of 6 and bas of 9 units of the right triangle.

Pythagorean formula:

c=√a²+b²

Now, insert values and calculate as follows:

c = √a²+b²

c = √9²+16²

c = 18.35 units

Therefore, we know that the required hypotenuse of the given right triangle is 18.35 units from the Pythagorean theorem.

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Complete question:

A right triangle has a base of 9 and a height of 16. Calculate hypotenuse.

A basis for the subspace of R4 consisting of all vectors perpendicular to v is [-7/9, 1, 0, 0], [-2/9, 0, 1, 0], [1/3, 0, 0, 1].

We can find a basis for the subspace of R4 consisting of all vectors perpendicular to v by solving the homogeneous system of linear equations Ax = 0, where A is the matrix whose rows are the components of v and x is a column vector in R4.

The augmented matrix [A|0] is:

| 9 7 2 -3 | 0 |

||

||

||

||

We can row reduce the augmented matrix using elementary row operations to get it in reduced row echelon form.

| 1 7/9 2/9 -1/3 | 0 |

||

||

||

||

We can write the solution as a parametric vector form:

x1 = -7/9s - 2/9t + 1/3u

x2 = s

x3 = t

x4 = u

where s, t, and u are arbitrary constants.

Therefore, a basis for the subspace of R4 consisting of all vectors perpendicular to v is:

[-7/9, 1, 0, 0], [-2/9, 0, 1, 0], [1/3, 0, 0, 1]

These vectors are linearly independent and span the subspace of R4 perpendicular to v.

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that is a coefficent

Answer:

2.5 years

Step-by-step explanation:

Given data

P=9000

r= 1.25%

A= 9281.25

The simple interest expression is given as

A=P(1+rt)

substitute

9281.25= 9000(1+0.0125*t)

9281.25=9000+112.5t

collect like terms

9281.25-9000=112.5t

281.25= 112.5t

t= 281.25/112.5

t= 2.5

Hence the time is 2.5 years

Answer:

Step-by-step explanation

To find the amount of rain the meteorologist predicted, start by listing the key information from the problem.

The actual amount of rain was 1.5 inches.

The meteorologist's prediction was 20% less than that. This is the percent error.

First, find the amount of error. It is 20% of the actual amount of rain.

0.21.5=0.3

So, the amount of error in the meteorologist's prediction is 0.3 inches. Since the predicted amount was less than the actual amount, subtract 0.3 from the actual amount of rain.

1.5–0.3=1.2

The meteorologist predicted 1.2 inches of rainfall.

You could also find the meteorologist's rainfall prediction by finding 80% of the actual amount of rain.

0.81.5=1.2

The amount of rainfall the meteorologist predict is 1.2 inches

From the question, we have the following parameters that can be used in our computation:

Amount of rainfall = 1.5 inches

Prediction = 20% less than the amount of rainfall

These parameters imply that:

Prediction = Amount of rainfall * (1 - Percentage less)

Substitute the known values in the above equation, so, we have the following representation

Prediction = 1.5 * (1 - 20%)

Evaluate

Prediction = 1.2

Hence, the prediction is 1.2 inches

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Answer:

Ratio of student who signed up for art club:

1/5

Ratio who signed other club:

4/5

Step-by-step explanation:

First find out ratio who signed up for art club

you have 16 out of 80

find the common factor: 16

16/16 = 1

80/16 = 5

so 1/5

other clubs is the rest so 5/5 - 1/5 = 4/5

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The probability of choosing a blue or yellow highlighter when a yellow highlighter is picked is 17/25.

Here, according to the question:

Total number of yellow highlighters  = 12

Total number of blue  highlighters  = 6

Total number of green highlighters  = 4

Total number of orange  highlighters  = 3

∴ Total number of highlighters  =  12 + 6 + 4 + 3  = 25

Let E1: Event of selecting yellow highlighter.

P(E1) = \(\frac{Total number of yellow highlighters}{Total highlighters}\) = \(\frac{12}{25}\)

Let E2: Event of selecting blue or yellow highlighter one yellow highlighter is selected.

∴Total yellow highlighters left after selecting one = 12 -1  = 11

Also, the number of blue highlighters = 6

So, the TOTAL FAVORABLE to E2 = 6+ 11 = 17

P(E2)  = \(\frac{Total number of yellow + blue highlighters}{Total highlighters}\) = \(\frac{17}{25}\)

Hence, The probability of choosing a blue or yellow highlighter when a yellow highlighter is picked is 17/25.

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Answer:

x=-10

Step-by-step explanation:

2(x+3)=x-4

2x+6=x-4

-2x   -2x

6=-x-4

+4    +4

10=-x

-1    -1

-10=x

\( \Large{\boxed{\sf x = 10}} \)

\( \\ \)

Given equation:

\( \sf 2(x + 3) = x - 4 \)

\( \\ \)

Expand the left side using the following distributive property:

A(B + C) = AB + AC

\( \\ \)

Here, A = 2, B = x, and C = 3.

We get:

\( \sf 2(x) + 2(3) = x - 4 \\ \\ \sf 2x + 6 = x - 4 \)

\( \\ \)

Now, subtract 6 from both sides:

\( \sf 2x + 6 - 6 = x - 4 - 6 \\ \\ \sf 2x = x - 10 \)

\( \\ \)

Subtract x from both sides :

\( \sf 2x - x = x - 10 - x \\ \\ \\ \boxed{\boxed{\sf x = -10}} \)

\( \\ \\ \)

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Answer:

it's easier the ramp because although it is steeper it is more of stable ground

The number of ways in which the 8 teams finish found by permutation is 1st, 2nd, 3rd is 336.

A permutation would be a mathematical computation of the number of possible arrangements of a given set, in which the sequence of the arrangements is important.

Now, according to the question,

We have ten teams and want to understand number of times PERMUTATIONS OF 3 are possible.  For only a PERMUTATION, we want to consider how several positions we are selecting and how many options are available for each of those positions.

So, given three options are;

(# of choices for first) x (# of choices for second) x (# of choices for third)

If there are originally 8 teams to pick from, then first place has 8 alternatives. When one of those is chosen for first, there are only 7 alternatives for second, and only 6 choices for third... and so on.

8 × 7 × 6 = 336

Therefor, here are 366 possible methods to choose first, second, and third place from the original eight teams.

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Answer:

Distance xy = 11.66 unit (Approx)

Step-by-step explanation:

Given:

x(-7,10)

y(3,4)

Find:

Distance xy

Computation:

Distance = √(x2-x1)²+(y2-y1)²

Distance xy = √(3+7)²+(4-10)²

Distance xy = √ 100 + 36

Distance xy = 11.66 unit (Approx)

Yes, if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

What is AAS congruence rule?

AAS congruence rule or theorem states that if two angles of a triangle with a non-included side are equal to the corresponding angles and non-included side of the other triangle, they are considered to be congruent.

Let us see the proof of the theorem:

Given: AB = DE, ∠B=∠E, and ∠C =∠F. To prove: ∆ABC ≅ ∆DEF

If both the triangles are superimposed on each other, we see that ∠B =∠E and ∠C =∠F. And the non-included sides AB and DE are equal in length. Therefore, we can say that ∆ABC ≅ ∆DEF.

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Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

can you heart this so i can get some point for my homework

Step-by-step explanation:

The term you're looking for is "uncertain digits."

Uncertain digits refer to the digits in a measurement that exceed the level of certainty provided by the measuring instrument.

Measurements, it is crucial to recognize the limitations of the instruments being used, as this can impact the precision and accuracy of the results.
Precision is the degree to which an instrument can consistently produce the same measurement, while accuracy is the closeness of a measurement to its true value.

Uncertain digits can affect both of these aspects.
To better understand uncertain digits, consider the following step-by-step explanation:
Identify the measuring instrument:

This could be a ruler, thermometer, or any other device used to take measurements.
Determine the instrument's least count:

The least count is the smallest unit the instrument can measure.

A ruler with millimeter markings has a least count of 1 millimeter.
Record the measurement:

When taking a measurement, include all the certain digits (those within the instrument's least count) and one uncertain digit.

The uncertain digit is an estimate, and it represents the best guess within the least count of the instrument.
Keep in mind the limitations:

Recognize that uncertain digits are an inherent part of the measuring process and that they affect the precision and accuracy of the results.
Uncertain digits are the digits that exceed the certainty of a measuring instrument.

It is important to consider these digits and the limitations of the instruments used when conducting experiments or making measurements.

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Answer:

4 hours/30 min=12

-2*12=-24

6-24=-18

-18°C

Step-by-step explanation:

The correct formula for the probability of the union of two events, A and B, is:\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

The probability of the union of two events, denoted as \(P(A \cup B)\), represents the probability that either event A or event B (or both) occur.

When events A and B are mutually exclusive, it means that they cannot happen at the same time. In this case, if event A occurs, event B cannot occur, and vice versa. Therefore, the probability of their union is simply the sum of their individual probabilities:

This is because there is no overlap or intersection between the two events.

To account for the overlap, we subtract the probability of their intersection, denoted as \( P(A \cap B) \), from the sum of their individual probabilities:

By subtracting \( P(A \cap B) \), we remove the duplicate probability associated with the overlapping region, ensuring that it is only counted once.

Therefore, the correct formula for the probability of the union of two events considers both the individual probabilities and the intersection of the events.

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The value of the area of the triangle ABC is 80 square units

The given dimensions of the triangle are

Base = 8 unts

Height = 20 units

Mathematically, the area of a triangle can be represented as

Area = 0.5 * Base * Height

When the given values are substituted into the above equation, we have

Area = 0.5 * 8 * 20

Evaluating the products, we have

Area = 80

Include the units

Area = 80 square units

So, the calculated area of the triangle is 80 square units

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Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

Answer:

341

Step-by-step explanation:

First, divide 51 by 3 to get 17.

So the problem should be 315-17+43.

Then, do 315-17 and get 298.

Lastly, add 43 to get the answer of 341.

Answer:(

2,−6).(9,9)

(,8).(7,−52)

(12,−5)−(5,6)

Step-by-step explanation:

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