The distance, D, travelled by a particle is directly proportional to the square of the time, t, taken. When t = 40, D = 30. find a formula for D in terms of t. Calculate the value of D when t = 64​

Answer:

0.18 or 0.14 or 0.10

Step-by-step explanation:

s = {(-5, 7)} cannot be a basis for R^2 because it does not satisfy the three requirements of a basis: having at least two linearly independent vectors, containing only linearly independent vectors, and spanning the entire vector space.

The set s = {(-5, 7)} is not a basis for R^2 (the two-dimensional real vector space) for several reasons:

Cardinality: A basis for a vector space must contain at least two linearly independent vectors. Since s contains only one vector, it cannot be a basis for R^2, which has dimension 2.

Linear independence: A basis must contain linearly independent vectors. If a vector in the basis can be written as a linear combination of the other basis vectors, it is not linearly independent, and the set cannot be a basis.

Spanning: A basis must span the entire vector space, meaning that every vector in the vector space can be written as a linear combination of the basis vectors. The set s = {(-5, 7)} does not span R^2 because it contains only one vector, and not every vector in R^2 can be written as a scalar multiple of this vector.

Therefore, s = {(-5, 7)} cannot be a basis for R^2 because it does not satisfy the three requirements of a basis: having at least two linearly independent vectors, containing only linearly independent vectors, and spanning the entire vector space.

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Sally purchased 7 pieces of orange .

Conversion applied :

1 dollar = 100 cents

Cost of 1 piece of orange = 51 cents

Cost of 1 piece of apple = 42 cents

Let pieces of orange purchased be x .

⇒ pieces of apples purchased = 11 - x .

The following linear equation becomes ,

51 x + 42 ( 11 - x ) = 5.25 * 100

Solving linear equation in 1 variable given above ,

9 x = 63

x = 7

⇒ no. of oranges purchased = 7

Therefore Sally purchased 7 pieces of orange .

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The distance equation is related to the Pythagorean theorem in that it is derived from it, and both can be used to find the distance between two points in a Cartesian plane.

The distance equation is related to the Pythagorean theorem by its derivation and usage. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem can be used to calculate the distance between two points in a Cartesian plane.

The distance equation is derived by using the Pythagorean theorem. If the coordinates of two points, say A and B, are (x1, y1) and (x2, y2) respectively, then the distance between them is given by:

\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

This equation is simply the Pythagorean theorem, where the hypotenuse is the distance between points A and B, and the other two sides are the horizontal and vertical distances between the points. The distance equation can also be used to find the length of the sides of a right triangle, as long as the coordinates of the endpoints are known.

In conclusion, the distance equation is related to the Pythagorean theorem in that it is derived from it, and both can be used to find the distance between two points in a Cartesian plane.

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Answer:

y= −x−5

Step-by-step explanation:

the equation for a rational function with the given characteristics calculator is y = -10 (x - 1)² / (x - 2)

Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomial coefficients don't have to be rational numbers; they can be taken in any field. K

Vertical asymptote at, x = 2

So, (x - 2) will be in the denominator

Double zero at x = 1

So, (x - 1)² will be in the numerator.

So, y = a (x - 1)² / (x - 2)

at x = 0, y = 5

So, 5 = a (-1)² / (-2)

Therefore, a = -10

So, y = -10 (x - 1)² / (x - 2)

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COMPLETE QUESTION:

Write an equation for a rational function with the given characteristics. Vertical asymptote at x = 2, double zero at x = 1, y-intercept at (0,5)

y =

Answer:

a length ★ bright

(14★8)m =112m²

b. (4+2+8+14+8+5)m

=41m

The first step to solve this exercise is to write the Mixed number as a decimal number. You can do it by dividing the numerator by the denominator of the fractional part and adding the quotient to the Whole number part, as follows:

So:

Knowing that Positive numbers are greater than zero and knowing that Negatives numbers are less than zero, we can order the given numbers from greatest to least, as you can see below:

Based on the given data, the probability of a room being occupied on any particular weekend night is 0.75. To calculate the probability that at least 4 out of the 7 rooms are occupied on a weekend night, we can use the binomial probability formula. By summing up the probabilities for 4, 5, 6, and 7 occupied rooms, we find that the probability is approximately 0.923.

To calculate the probability, we can use the binomial probability formula, which states that the probability of getting exactly k successes in n independent Bernoulli trials, each with a probability p of success, is given by the formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

In this case, we want to find the probability of at least 4 out of 7 rooms being occupied on a weekend night. We can calculate this by summing up the probabilities of getting 4, 5, 6, and 7 occupied rooms.

For 4 occupied rooms:
P(X = 4) = (7 choose 4) * 0.75^4 * (1 - 0.75)^(7 - 4) = 0.339

For 5 occupied rooms:
P(X = 5) = (7 choose 5) * 0.75^5 * (1 - 0.75)^(7 - 5) = 0.395

For 6 occupied rooms:
P(X = 6) = (7 choose 6) * 0.75^6 * (1 - 0.75)^(7 - 6) = 0.266

For 7 occupied rooms:
P(X = 7) = (7 choose 7) * 0.75^7 * (1 - 0.75)^(7 - 7) = 0.122

To find the probability of at least 4 occupied rooms, we sum up the probabilities for 4, 5, 6, and 7 occupied rooms:

P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.339 + 0.395 + 0.266 + 0.122 = 0.923

Therefore, the probability that at least 4 out of the 7 hotel rooms are occupied on any weekend night is approximately 0.923, or 92.3% when rounded to three decimal places.

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Based on the given data, the probability of a room being occupied on any particular weekend night is 0.75.

To calculate the probability that at least 4 out of the 7 rooms are occupied on a weekend night, we can use the binomial probability formula. By summing up the probabilities for 4, 5, 6, and 7 occupied rooms, we find that the probability is approximately 0.923.

To calculate the probability, we can use the binomial probability formula, which states that the probability of getting exactly k successes in n independent Bernoulli trials, each with a probability p of success, is given by the formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

In this case, we want to find the probability of at least 4 out of 7 rooms being occupied on a weekend night. We can calculate this by summing up the probabilities of getting 4, 5, 6, and 7 occupied rooms. For 4 occupied rooms:
P(X = 4) = (7 choose 4) * 0.75^4 * (1 - 0.75)^(7 - 4) = 0.339

For 5 occupied rooms:
P(X = 5) = (7 choose 5) * 0.75^5 * (1 - 0.75)^(7 - 5) = 0.395
For 6 occupied rooms:
P(X = 6) = (7 choose 6) * 0.75^6 * (1 - 0.75)^(7 - 6) = 0.266
For 7 occupied rooms:
P(X = 7) = (7 choose 7) * 0.75^7 * (1 - 0.75)^(7 - 7) = 0.122
To find the probability of at least 4 occupied rooms, we sum up the probabilities for 4, 5, 6, and 7 occupied rooms:

P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.339 + 0.395 + 0.266 + 0.122 = 0.923. Therefore, the probability that at least 4 out of the 7 hotel rooms are occupied on any weekend night is approximately 0.923, or 92.3% when rounded to three decimal places.

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Answer:

50 children tickets; 60 adult tickets

Step-by-step explanation:

Let a = number of adult tickets.

Let c = number of children tickets.

a + c = 110

5a + 3c = 450

  -3a - 3c = -330

  5a + 3c = 450

------------------------

   2a        = 120

a = 60

a + c = 110

c = 50

Answer: 50 children tickets; 60 adult tickets

The statement "a. The slope is negative" is true about the slope of the least squares regression line when the correlation coefficient is negative.

When the correlation coefficient is negative, it indicates an inverse relationship between the two variables. In a linear regression, the slope of the line represents the direction and magnitude of the relationship between the independent and dependent variables. A negative correlation coefficient indicates that as the independent variable increases, the dependent variable decreases. Therefore, the slope of the least squares regression line will also be negative.

The slope of the regression line is calculated using the formula: slope = correlation coefficient * (standard deviation of y / standard deviation of x). Since the correlation coefficient is negative and the standard deviation of x and y are positive values, multiplying a negative correlation coefficient by positive standard deviations will result in a negative slope. Hence, option "a. The slope is negative" is the correct statement.

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T A can be seen as a linear transformation from R^2 to R^3.

To find the range and codomain of the matrix transformation T A, we need to first determine the matrix T A . The matrix T A is obtained by multiplying the input vector x by A:

T A (x) = A x

Therefore, T A can be seen as a linear transformation from R^2 to R^3.

To determine the range of T A , we need to find all possible outputs of T A (x) for all possible inputs x. Since T A is a linear transformation, its range is simply the span of the columns of A. Therefore, we can find the range by computing the reduced row echelon form of A and finding the pivot columns:

A =  (\left[\begin{array}{cc}1 & 2 \ 1 & -2 \ 0 & 1\end{array}\right]) ~ (\left[\begin{array}{cc}1 & 0 \ 0 & 1 \ 0 & 0\end{array}\right])

The pivot columns are the first two columns of the identity matrix, so the range of T A is spanned by the first two columns of A. Therefore, the range of T A is the plane in R^3 spanned by the vectors [1, 1, 0] and [2, -2, 1].

To find the codomain of T A , we need to determine the dimension of the space that T A maps to. Since T A is a linear transformation from R^2 to R^3, its codomain is R^3.

If the functions were not linear, it would not make sense to talk about their range or codomain in this way. The concepts of range and codomain are meaningful only for linear transformations.

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Answer:

D- 224

Step-by-step explanation:

10% of 140 is 14

So then you multiply 14 by 6 to get 60%

then you add that to 140 to equal 224.

The correct statement is that if the sales of burgers at Nick's Burgers increases by 60%, the total sales per day will be increased to 224 burgers per day from 140 burgers per day.

An increase in sales refers to as the positive shift in the sales of goods as compared to previous sessions during a given period of time, given that other factors vary.

The increase in sales will happen as a result of the strategies that may have been adopted by Nick or increase in the demand due to external factors.

The calculation of increased no. of burgers sold per day can be calculated by using the formula and putting the values given in the example as below,

increased sales  = 224

So, the new sales of burgers per day is calculated as 224 per day.

Hence, an increase in sales of burgers at Nick's by 60% will result in sales of 224 burgers per day from 140 burgers per day.

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Answer:

8589465 pages are unread

Step-by-step explanation:

nidhi's hobby is reading moral value books

plz mark as brainliest if it helps

Answer:

8589465 unread pages

Step-by-step explanation:

No. of songs in the playlist of Lashondra, Harriet and Velora are 522, 58 and 406 respectively.

songs in Harriet's playlist = x

LaShondra's playlist has nine times as many songs as Harriet playlist

= 9x

Velora has seven times as many songs on the playlist as Harriet  = 7x

total songs in combine playlist = 986

x + 9x + 7x = 986

17x =  986

x = 986/17

x = 58

songs in the playlist of Lashondra = 9x = 9 x 58 = 522

songs in the playlist of Harriet        = x = 58

songs in the playlist of  Velora        =  7x = 7 x 58 = 406

No. of songs in the playlist of Lashondra, Harriet and Velora are 522, 58 and 406 respectively.

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The key features of the quadratic function include the following:

a. vertex: (4, -18).

b. domain: [-∞, ∞].

c. Range: [-18, ∞].

d. Axis of symmetry: x = 4.

e. x-intercepts: (-2, 0) and (10, 0).

f. y-intercept: (0, -10).

g. Minimum value: -18.

h. Equation of the function: y = 2(x - 4)² - 18.

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided about the vertex (4, -18) and the y-intercept (0, -10), we can determine the value of "a" as follows:

y = a(x - h)² + k

-10 = a(0 - 4)² - 18

18 - 10 = 4a

8 = 4a

a = 8/4

a = 2.

Therefore, the required quadratic function in vertex form is given by:

y = a(x - h)² + k

y = 2(x - 4)² - 18

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The mathematical model that best fits the given data is option : y = 82.3 - 8.275x.

To construct a scatterplot and determine the mathematical model that best fits the given data, we will plot the points and analyze the trend.

Given Data:

x: 4, 8, 12, 16, 20

y: 40, 20, -11, -37, -97

Let's plot these points on a scatterplot:

(x, y) points:

(4, 40)

(8, 20)

(12, -11)

(16, -37)

(20, -97)

After plotting the points, we can analyze the trend in the data.

By observing the scatterplot, it is clear that a linear or quadratic model would not fit the data well since the points do not follow a straight line or a parabolic curve.

Next, we can try the logarithmic, exponential, and power models to see if any of them fit the data better.

Using a calculator or computer to perform the regression analysis, we find that the regression equation with the highest R² value is:

y = 82.3 - 8.275x

This equation corresponds to option : y = 82.3 - 8.275x

The regression equation represents a linear model that best fits the given data. The R² value indicates how well the model explains the variability in the data, and in this case, the linear model provides the highest R² value compared to the other models.

It's important to note that the specific values of the coefficients in the regression equation may vary slightly depending on the calculator or software used for the analysis. However, the overall best-fit model remains the same.

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Answer:

Step-by-step explanation:

Given,

ABC is a triangle in which I is the incenter of the triangle.

Solution,

Since I is the incenter of the triangle.

Incenter is the point where three angle bisectors of the triangle meets.

so AI = BI = CI

\(3x+7=5x-11\\5x-3x=7+11\\2x=18\\x=9\)

So,

Thus the value of x is 9.

Answer:

x = 9

Step-by-step explanation:

The incenter of a triangle is the point of intersection of all the three interior angle bisectors.

The distance from the incenter to the sides of the triangle is equal.

Therefore: AI = BI = CI

Equate the measures of AI and BI, and solve for x:
⇒ AI = BI

⇒ 3x + 7 = 5x - 11

⇒ 3x + 7 -5x = 5x - 11 - 5x

⇒ -2x + 7 = -11

⇒ -2x + 7 - 7 = -11 - 7

⇒ -2x = -18

⇒ -2x ÷ -2 = -18 ÷ -2

⇒ x = 9

This situation should be analyzed using a two-sample independent method. The two-sample independent method is used when comparing two independent groups, in this case, taxi ride times in San Diego and Phoenix. The two-sample paired method is used when comparing the same group under two different conditions, which is not the case here, as the taxi ride times are taken from two separate cities. There is no common characteristic that makes these data paired.

A two-sample independent method is used to compare the means of two independent populations, which is appropriate for this situation. The independent samples t-test is a common statistical test used to compare the means of two independent populations.On the other hand, if the data were obtained from the same set of taxis in both cities or from the same set of riders in both cities, then the situation would be a paired situation, and a two-sample paired method would be more appropriate.Paired data refers to data that is collected from the same sample, subject, or group at different points in time or under different conditions. For example, if the data were obtained from the same set of taxis in both cities, then the data would be paired because each taxi in San Diego would have a corresponding taxi in Phoenix. Similarly, if the data were obtained from the same set of riders in both cities, then the data would be paired because each rider in San Diego would have a corresponding rider in Phoenix.In summary, since the data in this situation were obtained from two different cities, a two-sample independent method is appropriate. If the data were obtained from the same set of taxis or riders in both cities, a two-sample paired method would be appropriate.

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Answer:

25% decrease

Step-by-step explanation:

=(60−80)|80|×100

=−2080×100

=−0.25×100

=−25%change

=25%decrease

Answer:

25% decrease

Step-by-step explanation:

Answer: A.

Step-by-step explanation: About 3 tsp of vanilla is used for every 1/3 cup of sugar.

Answer:

Step-by-step explanation:

Let x = the number of teaspoons of vanilla needed

sugar/vanilla: 2/3 = 1

6 x Cross multiply

(2/3)x = 6

x = 6(3/2)

x = 9 teaspoons.

Answer:

8 cm

Step-by-step explanation:

:)

Answer:

p(x) = (x - 5)(x + 1)(x + 4)

General Formulas and Concepts:

Algebra I

Algebra II

Step-by-step explanation:

*Note:

Please excuse my bad handwriting :)

Step 1: Define

Identify

p(x) = x³ - 21x - 20

Linear factor (x - 5)

Step 2: Factor

Option 1: Factoring cubes formula

Option 2: Long Division

See Attachment

Option 3: Synthetic Division

See Attachment #2

Answer:

77.77

Step-by-step explanation:

The new value =

77 + The value of the percentage increase =

77 + (1% × 77) =

77 + 1% × 77 =

(1 + 1%) × 77 =

(100% + 1%) × 77 =

101% × 77 =

101 ÷ 100 × 77 =

101 × 77 ÷ 100 =

7,777 ÷ 100 =

77.77

Answer:

= 77.77

Step-by-step explanation:

1% = 1/100 = 0.01

Then:

77*0.01 = 0.77

77 increased 1% is:

77 + 0.77 = 77.77

The area of the shaded triangle formed as the result of the overlap is = 62.35 inches ²

After folding the rectangle with length of 12 inches and width of 18 inches, an equilateral triangle was formed.

An equilateral triangle is a type of triangle where by all the three sides are equal.

To determine the value of one of the sides, CB or CD is used because the folding didn't affect these sides.

Using the formula for the area of an equilateral triangle,

A = √¾ a²

a= 12 inches

A = √¾ ×12²

A = 62.35 inches ²

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Answer:

Its 78!!!!

Solution:

1/2(12 * 18 - 5 * 12) = 78

Answer: 6/4x

Step-by-step explanation:

Slope = Change in y/Change in x

The future value of $12,250 after 8 years, with a 4% annual interest rate compounded quarterly, is approximately $16,495.11.

To calculate the future value of $12,250 after 8 years with an annual interest rate of 4% compounded quarterly, we can use the formula for compound interest:

FV = PV * (1 + r/n)^(n*t)

Where:

FV is the future value

PV is the present value (initial amount)

r is the annual interest rate (in decimal form)

n is the number of compounding periods per year

t is the number of years

Given:

PV = $12,250

r = 4% = 0.04 (as a decimal)

n = 4 (compounded quarterly)

t = 8 years

Plugging in these values into the formula, we get:

FV = $12,250 * (1 + 0.04/4)^(4*8)

= $12,250 * (1 + 0.01)^(32)

= $12,250 * (1.01)^(32)

Using a calculator, we can evaluate this expression to find the future value:

FV ≈ $12,250 * 1.349858807576003

FV ≈ $16,495.11

Therefore, the future value of $12,250 after 8 years, with a 4% annual interest rate compounded quarterly, is approximately $16,495.11.

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Answer:

Step-by-step explanation:

Given

Answer

Since it is given

KJ=KL

HK=HK (Common)

The only condition to show SSS congruency is HJ = HL