Line A passes through the points (0, -5) and 12,1. Line B passes through the points (0, -4) and (10, 1). write an equation for each line

Answer:

\(27436\pi\) square inches

Step-by-step explanation:

Since we are covering the surface of the ball, we need to determine the ball's surface area.

Assuming the ball to be a sphere, its surface area would be \(A=4\pi r^2\) where \(r\) is the radius.

Since the diameter is twice the radius, then the radius of the ball is 19 inches.

Therefore, the surface area of the ball is \(A=4\pi (19)^3=4\pi(6859)=27436\pi\) square inches.

Each squad has to have an equal amount of men and women. The maximum number of teams that can participate is 8.

A location in mathematics where a function has its maximum value. The value is an absolute maximum if it exceeds or is equal to all other function values. It is a relative or local maximum if it is simply greater than any neighboring point.

Number of girls = 16.

Number of boys = 20.

In order to calculate the maximum number of teams that can enter, we must determine the most prevalent criteria for both boys and girls based on the information provided. As follows:

Factors of 18 \(= 1, 2, 4, 8\)  and 16.

Factors of 24 = \(1, 2, 3, 4, 6, 8, 12\) and 24.

Highest common factor = 8

Therefore, the greatest number will be 8.

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Answer/Step-by-step explanation:

Surface area of cylinder = 2πrh + 2πr²

Surface area of the cylinder with,

height (h) = 4 ft

radius (r) = 5 ft

Surface area = 2*3.14*5*4 + 2*3.14*5²

= 125.6 + 157

= 282.6 ft²

Surface area of the cylinder with,

height (h) = 12 yd

radius (r) = 3 yd

Surface area = 2*3.14*3*12 + 2*3.14*3²

= 282.74 yd²

Answer:

If r-squared for the transformation is greater than r-squared for the original regression, the transformation is successful.

Step-by-step explanation:

The lengths of the sides of the triangle are 5, 12, and 13.

So the correct option is the last one.

Remember that if we have two points (x₁, y₁) and (x₂, y₂), the distance between these two points is given by the formula:

d = √( (x₁ - x₂)² + (y₁ - y₂)²)

Here we know that the vertices of our triangle are the points:

(0, 0), (5, 0), (5, 12)

And we want to find the lengths of the sides.

We can get the length of the first side using the points  (0, 0), (5, 0)

d₁ = √( (0 - 5)² + (0 - 0)²) = 5

The length of the second side is: (5, 0), (5, 12).

d₂ = √( (5 - 5)² + (0 - 12)²) = 12

The length of the third is side is given by the points (5, 12) and (0, 0)

d₃ = √( (5 - 0)² + (12 - 12)²)

d₃ = √(25 + 144) = 13

Then the correct option is the last one:

5, 12, 13.

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To determine how many times the spinner will land on blue or green, we need to know the number of sections that are shaded blue or green.

Let's assume the spinner has 8 sections in total, with 3 sections shaded blue, 4 sections shaded green, and the remaining sections shaded red.

Out of 24 spins, the probability of landing on blue or green can be calculated as the sum of the individual probabilities. The probability of landing on blue is 3/8, and the probability of landing on green is 4/8 (since there are 4 green sections out of 8 in total).

Therefore, the expected number of times the spinner will land on blue or green in 24 spins is:

(3/8 + 4/8) * 24 = (7/8) * 24 = 21.

So, the spinner is expected to land on blue or green approximately 21 times out of the 24 spins.

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Answer:

The answer is 7

because 40 times 7 is 280 then we double 7 to 14 because remember it says he paid 2 times his hourly rate after 40 hours so then we multipy 14 times 10 and it will give you 140 so then u add them to get his total of $420

Answer:

To find the number of boxes, divide the total order by the number of flash drives per box.

2,665/36

When you solve you get 74.027777….., however you can’t have part of a box, so you should round down to the nearest whole number. The nearest whole number is 74. It takes about 74 boxes to hold all of the flash drives.

:)

\(9 = -4x - 3\\9+3 = -4x\\-4x = 9 + 3\\-4x = 12\\x = \frac{12}{-4}\\ x = -3\)

Hope that helped!

Answer: No Triangle: 30 , 85 , 60, and 2, 8, 10

One Triangle: 7, 24, 25

Many Triangles: 45, 45, 90           5, 15, 160

a)  The direction in which you should walk to descend fastest is: (-12, -16)

b) The slope of your path is: -88

c) The direction of the greatest increase in temperature at the point (−2, 2) is: (-4, 4)

The maximum rate of change is: 4√2

d) The direction of the greatest decrease is: (4, -4).

The most negative rate of change is: 4√2

(a) The equation on the surface is:

z = 15 - (3x² + 2y²)

The gradient of this surface will be the partial derivatives of the equation. Thus:

Gradient of the surface z:

∇z = (-6x, -4y)

Since you are standing above the point (2,4), then the direction to descend fastest is:

∇z(2,4) = (-6(2), -4(4))

∇z(2,4) = (-12, -16)

That gives us the direction to descend fastest is in the direction.

(b) If you start to move in the direction (-12, -16) above, then slope of your path (rate of descent) is given by the dot product expressed as:

Slope = ∇z(2,4) · (-12, -16)

= (2)(-12) + (4)(-16)

= -24 - 64

= -88

(c) We want to find the direction of the greatest increase in temperature at the point (−2,2).

Thus, the gradient of T(x,y) is given by:

∇T = (2x, 2y).

The direction is:

∇T(-2, 2) = (2(-2), 2(2))

∇T(-2,2) = (-4, 4)

The maximum rate of change is:

∇T(-2,2) = √((-4)² + 4²)

= √(16 + 16)

= √(32)

= 4√2

(d) The direction of the greatest decrease is:

(-∇T(-2, 2)) = (-(-4), -4)

= (4, -4).

The most negative rate of change is:

∇T(-2, 2) = √(4² + (-4)²)

= √(16 + 16)

= √(32)

= 4√2

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a. the amount that the gymnast wins is a discrete random variable. b. the gymnast can expect to win $86,000 on average. c. the population variance of the amount that the gymnast wins is $708,000,000.

(a) A discrete random variable is a variable that can take on a countable number of distinct values. In this case, the random variable represents the amount that the gymnast wins. As the gymnast can win either a gold, silver, or bronze medal, the random variable can take on the values $100,000, $80,000, and $50,000, respectively. Therefore, the amount that the gymnast wins is a discrete random variable.

(b) To calculate the amount that the gymnast can expect to win, we need to find the expected value or the mean of the random variable. The expected value is calculated by multiplying each possible value of the random variable by its corresponding probability and summing them up.

Expected value (E) = (Probability of winning gold * Amount for gold) + (Probability of winning silver * Amount for silver) + (Probability of winning bronze * Amount for bronze)

E = (0.6 * $100,000) + (0.2 * $80,000) + (0.2 * $50,000)

E = $60,000 + $16,000 + $10,000

E = $86,000

Therefore, the gymnast can expect to win $86,000 on average.

(c) The population variance (σ^2) measures the spread or variability of the random variable. It is calculated by taking the sum of the squared differences between each value of the random variable and the expected value, weighted by their probabilities.

Variance (σ^2) = [(Value 1 - E)^2 * Probability 1] + [(Value 2 - E)^2 * Probability 2] + [(Value 3 - E)^2 * Probability 3]

Variance = [($100,000 - $86,000)^2 * 0.6] + [($80,000 - $86,000)^2 * 0.2] + [($50,000 - $86,000)^2 * 0.2]

Variance = [($14,000)^2 * 0.6] + [(-$6,000)^2 * 0.2] + [(-$36,000)^2 * 0.2]

Variance = $117,600,000 + $72,000,000 + $518,400,000

Variance = $708,000,000

Therefore, the population variance of the amount that the gymnast wins is $708,000,000.

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The dimensions of the photograph are found as 13 in and 6 in.

Let length = x.

So, width = x - 7

Area = length x width

A = x (x -7)

and A = 78 inches squared.

Thus,

78 = x (x -7)

On solving.

x² - 7x - 78 = 0

Find the factors of the quadratic equation,

x² - 7x - 78 = 0

(x - 13)(x + 6) = 0

Thus,

x = 13 and x = -6 but (x > 0)

Thus, when x = 13 in,

Width = x + 7

Width = 13 - 7

Width = 6 in

Thus, the dimensions of the photograph are found as 13 in and 6 in.

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Data:

Initial balance: c

intrest rate: r

time (months)=m

growth: b

c=$100

r=7%=0.07

To an exponential function you have the next general form:

In this case

y=b(m)

C=c

r=r

t=m

An effective sampling method is not cast doubt on the usefulness of the sample

The effective sample is a calculation of the approximate sample size needed to obtain the same degree of accuracy as a simple random sample. It is denoted mathematically by the formula n/D, where n represents the sample size and D denotes the design effect. It is employed as a means of condensing the volume of data.

Effective sample size calculations are mostly used for qualitative analyses of the sample size. The sample size calculates the total number of measurements or observations made during an experiment or survey. The effective sample size—rather than the actual sample size—is utilized in this assessment since it is thought that a sample size of 30 is necessary for an analysis to be valid.

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Answer:

7502040

Step-by-step explanation:

you can have 6 women,5 women and 1 men,4 women and 2 men,

in first case,you can place women in 15*14*13*12*11*10 ways

in second case

15*14*13*12*11*7

and in third case

15*14*13*12*7*6

and you need to sum all this numbers

Answer:

81.7 in (nearest tenth)

Step-by-step explanation:

\(\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}\)

Given:

Substituting given value into the formula:

\(\begin{aligned}\implies \textsf{Circumference} & =2 \pi \cdot 13\\ & = 26 \pi\\ & = 81.7\: \sf in\:(nearest\:tenth)\end{aligned}\)

Answer:

8+2g

Step-by-step explanation:

Answer:

−27x5

Step-by-step explanation:

Answer:

6x^3

Step-by-step explanation:

Answer:

x and y connect in the orgin therfore

the value of y and x is equal that mean 0

Answer:

answer is 0.

y = x

when x = 0

y = 0.

Answer: The interest and amount to be paid at the end of 3 years is Rs.8700

Step-by-step explanation:

let P ,R, T be the Principle amount , Rate of interest and Time

             P= 6000rs

             R= 15%

             T=3 years

                      =6000rs×15r×3t÷100

                       =2700rs

                                                             = 8700rs

Answer:

2/5  or 0.4 pound for 1 can

Step-by-step explanation:

Divide the number of pound by the number of cans to know how much pound per can  2/5 = 0.4

       OR  

5 cans ------------2 pounds

1 can------------------x

Cross multiplication

5x = 2

x= 2/5

From the chi-square test, the p-value is greater than significance level so, we can't reject the null hypothesis. The distribution of patients in this data set of wards in community hospital has not changed.

We have a community hospital is studying its distribution of patients. Random sample with

number of patients = 317

There is a table present in above figure contains the type of patients, old rate and present rate of occurrence of type of patients.

Level of significance = 0.05

We have to test the claim that the distribution of patients in these ward is same or not.

Now, For testing the claim we will use the chi-square test, null and alternative hypothesis are defined as \(H_0\): the distribution of patients has not Changed

\(H_a\): the distribution of patients has Changed

Patients observed Expected

Maternity ward 65 20% of 317 = 63.4

Cardiac ward 100 32% of 317 = 101.44

burn ward 29 10% of 317 = 31.7

children ward 48 15% of 317 = 47.55

All wards 75 23% of 317 = 72.91

Now, calculate the χ² statistic : \(χ² = \frac{ \sum( O_i - E_i)²} {E_i}\)

where, Oᵢ --> observed value for iᵗʰ

Eᵢ --> excepted value for iᵗʰ

\(χ² = \frac{ \sum( 65 - 63.4)²} {63.4} + \frac{ \sum( 100 - 101.44)²} {101.4} + \frac{ \sum( 29 - 31.7)²} {31.7} + \frac{ \sum( 48 - 47.55)²} {47.55} + \frac{ \sum( 75 - 72.91)²} {72.91} \\ \)

= 0.355

Now, we calculate p-value for χ² > 0.355, from the calculater the critical value for

\(χ² = 0.355\) and degree of freedom = n - 1 = 5 - 1 = 4 , where 5 is number of categorical variables. So, \( P( χ² > 0.355)\) = 0.99

Since, the p-value = 0.99 > 0.05, so we fail to reject the null hypothesis. Hence, from the above test we can accept the claim that the distribution of patients has not changed.

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Complete question:

the community hospital is studying its distribution of patients. a random sample of 317 patients presently in the hospital gave the following information: type of patient, old rate of occurrences of these types of patients and present number of occurrence of type of patients. Using a 5% level of significance, test the claim that the distribution of patients in these wards has not changed.

If we know that f(-4) = 0, we can say that:

x + 4 is a factor of the function f(x).

This is because when we substitute x = -4 into the function, we get:

f(-4) = (-4)^4 + 2(-4)^3 - 9(-4)^2 - 2(-4) + 6 = 0

This means that (x + 4) is one of the factors of the function.

Now, we can use polynomial division or synthetic division to find the other factors. If we divide the function f(x) by (x + 4), we obtain:

           x^3 - 2x^2 - 17x + 3

We can use the Factor theorem on this cubic function f(x) = x^3 - 2x^2 - 17x + 3.

If we try to substitute a = 1 we find that f(1) = -15 which is not zero. If we try to substitute a = -1, we find that f(-1) = 23 which is not zero.

Now we can solve as follows:

Let x = t - 2/3. After substitution we get a cubic equation.

t^3 -25/3 t - 85/27 = 0

We can find one root of this cubic by rational root theorem which is t = 5 or t = -17/3.

Now, we can use synthetic division again to divide f(x) by the binomial (x - 5). This gives us:

        (x - 5)(x^2 + 3x - 1)

Therefore, the complete factorization of f(x) is:

f(x) = (x + 4)(x - 5)(x^2 + 3x - 1)

Therefore, the zeros of the function are:

x = -4, 5, (-3 ± √13)/2

Thus, these are the zeros of the polynomial.

Number of ways an art collector who owns 10 original paintings leave these paintings to three heirs are 120.

As given in the question,

Total number of paintings owned by an art collector = 10

Number of heirs whom an art collector willing to leave these paintings = 3

Number of ways an art collector who owns 10 original paintings leave these paintings to three heirs is equal to

= ¹⁰C₃

= ( 10 )! / ( 10 - 3 )! 3!

= ( 10 )! / 7! 3!

= ( 10 × 9 × 8 × 7! ) / 7! 3!

=  ( 10 × 9 × 8 ) / ( 3 × 2 × 1 )

= 120 ways

Therefore, number of ways an art collector who owns 10 original paintings leave these paintings to three heirs are 120.

The complete question is :

An art collector who owns 10 original paintings is preparing a will. In how many ways may the collector leave these paintings to three heirs?

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Answer: r = -0.14 ; weak correlation

Answer:

\(16x^2+25y^2-400=0\)

Step-by-step explanation:

Given:

There are 4 types of conic sections:

The definition of an ellipse is:

Therefore, the given definition is one for an ellipse.

\(\boxed{\begin{minipage}{7.4 cm}\underline{General equation of an ellipse}\\\\$\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$\\\\where:\\\phantom{ww}$\bullet$ $(h,k)$ is the center. \\ \phantom{ww}$\bullet$ $(h\pm a,k)$ or $(h,k\pm b)$ are the vertices. \\ \phantom{ww}$\bullet$ $(h\pm c,k)$ or $(h,k\pm c)$ where $c^2=a^2-b^2$.\\\end{minipage}}\)

As the given foci are (-3, 0) and (3, 0), they are on the x-axis. Therefore:

Therefore, the major axis is on the x-axis and the vertices are (h±a, k) and the co-vertices are (h, k±b).

The constant is the major axis which is 2a.  Given the constant is 10:

\(\implies 2a=10\)

\(\implies a=5\)

Since c² = a² - b²:

\(\implies 3^2=5^2-b^2\)

\(\implies b^2=5^2-3^2\)

\(\implies b^2=25-9\)

\(\implies b^2=16\)

Therefore, the equation for the conic section (ellipse) is:

\(\implies \dfrac{(x-0)^2}{5^2}+\dfrac{(y-0)^2}{16}=1\)

\(\implies \dfrac{x^2}{25}+\dfrac{y^2}{16}=1\)

In standard form:

\(\implies 25 \cdot \dfrac{x^2}{25}+25 \cdot \dfrac{y^2}{16}=25 \cdot 1\)

\(\implies x^2+\dfrac{25}{16}y^2=25\)

\(\implies 16 \cdot x^2+16 \cdot \dfrac{25}{16}y^2=16 \cdot 25\)

\(\implies 16x^2+25y^2=400\)

\(\implies 16x^2+25y^2-400=400-400\)

\(\implies 16x^2+25y^2-400=0\)

In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

For example,

[

1

9

−

13

20

5

−

6

]

{\displaystyle {\begin{bmatrix}1&9&-13\\20&5&-6\end{bmatrix}}}

is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a "

2

×

3

{\displaystyle 2\times 3} matrix", or a matrix of dimension

2

×

3

{\displaystyle 2\times 3}.

A possible basis for the space of symmetric 2 x 2 matrices is {
[1 0; 0 0], [0 1; 1 0], [0 0; 0 1] }.

There are three elements in the basis.
Hi! A basis for the space of symmetric 2 x 2 matrices can be represented using the following three matrices:

1. [1, 0]
  [0, 0]

2. [0, 1]
  [1, 0]

3. [0, 0]
  [0, 1]

These matrices are symmetric because their transposes (A^T) are equal to themselves (A). There are three elements in this basis.

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