Write the equation of the graph below in slope intercept form.

(2,0) and (0,-3)

Step by step

Large MAD tells us that the average distance between each data value and the mean is large.

Given that;

The mean age of swimmers for all of these teams is 10.

Since, MAD is the mean absolute deviation (MAD) of a set, it tells the average distance between each data value and the mean.

Hence, It is a method to express the variance in the data set.

So, the large MAD tells us that the average distance between each data value and the mean is large.

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Answer:

y= -1/2x + 1/2

Step-by-step explanation:

First, use the point-slope formula: y-y1 = m(x-x1)

y-2 = -1/2(x-(-3))

y-2= -1/2x + -1.5

(subtract 2 from both sides)

y = -1/2x + 1/2

The total area of the figure in this problem is given as follows:

41.3 ft².

The area of the composite figure is given by the sum of the areas of all the parts that compose the figure.

The figure in this problem is composed as follows:

Then the area of the triangle is given as follows:

At = 0.5 x 6 x 3 = 9 ft².

The area of the semicircle is given as follows:

Ac = π x 3² = 28.3 ft².

The area of the square is given as follows:

As = 2² = 4 ft².

Then the total area of the figure is given as follows:

9 + 28.3 + 4 = 41.3 ft².

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To find the critical value (t_c) for a given confidence level (c = 0.90) and sample size (n = 16), you will need to use the t-distribution table or an online calculator.

In this case, you have 15 degrees of freedom (n-1 = 16-1 = 15) and a confidence level of 90%.

Looking up these values in the t-distribution table or using an online calculator, you will find the critical value t_c to be approximately 1.753.

So, t_c = 1.753 (rounded to the nearest thousandth).

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Answer:

-24

Step-by-step explanation:

Step-by-step explanation:

steps are in the picture.

Answer:

the amount due for 3 hours would be $52 + ($34/hr)(3 hrs) = $154

Step-by-step explanation:

Write two equations, one for the total cost payable to Water R Us and another to Clogs:  

$52 + ($34/hr)t  =  $34 + ($40/hr)t, or

$18 = ($6/hr)t, which tells us that t = 3 (That's 3 hours).

At the time the charges from the two companies would be the same (3 hours into the job), the amount due for 3 hours would be

$52 + ($34/hr)(3 hrs) = $154

Answer:

D

Step-by-step explanation:

the graph of y=-3x + 4 is linear, meaning it forms a line

a line extends indefinitely in both directions, indicating an infinite amount of solutions; any point on the line would be a solution

Answer:

1.48 meters

Step-by-step explanation:

let the sum of the heights of the girls and the boys be Y and x respectively

\( \frac{x}{14} = 1.56 \: \: \: \: \frac{x + y}{32} = 1.515 \: \\ x = 21.84 \: \: \: \: x + y = 48.48 \\ y = 48.48 - 21.84 = 26.64 \\ \: the \: number \: of \: girls \: in \: aclass \: is \: 32 - 14 = 18 \\ then \: the \: mean \: will \: be \: \\ \frac{26.64}{18} = 1.48\)

X=6 x+y=

Answer:

mean (average height) of the girls is 1.48 metres

Step-by-step explanation:

Number of boys × average height  = 14 × 1.56 = 21.84

All students × average height = 32 × 1.515= 48.48

Number of girls × average height = 18 x

32-14 boys = 18 girls

Total height of all = Total height of boys + Total height of girls

 48.48 = 21.84 + 18x

48.48 - 21.84 = 18x

   26.64 = 18x

  26.64 ÷ 18 = x

           1.48 = x the average height of the girls

The number of coins that are mistakes in 20 days are 12000000

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

Mistake on 3% of the coins

Rate = 20000000 coins a day,

This means that

Mistakes = 3% * 20000000 * days

For the coins that are mistakes in 20 days, we have

Mistakes = 3% * 20000000 * 20

Evaluate

Mistakes = 12000000

Hence, the coins are mistakes in 20 days are 12000000

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Answer:

7

Step-by-step explanation:

15x is money for the people who have 3 course meals

12(10-x) =  120-12x is money for the people who have 2 courses.

15x+120-12x = 141

3x+120 = 141

3x = 21

x = 7

7 three course meals

comment if you need further explanation. I am here to help.

a) 4x + 2x = 6x - 4

= 6x = 6x - 4

cannot be solved further.

b) 3(2x + 4) = 2(2x - 4)

= 6x + 12 = 4x - 4

(bring the numbers and variables on one side)

= 6x + 4x = 12 - 4

10x = 8

x = 8/10 = 4/5

can be solved.

c) 5(x - 3) = 5x - 3

= 5x - 15 = 5x - 3

= (bring the variables and numbers on one side)

5x + 5x = -15 - 3

= 10x = -18

x = -18/10 = 9/5

can be solved

d) 2x = 2x + 4

= 2x + 2x = 4

= 4x = 4

x = 4/4 OR 1.

The probability of receiving two calls in a 5-minute interval is:

P(X = 2) = (e^-4 * 4^2) / 2! = 0.0902

The probability of receiving exactly 10 calls in 15 minutes is:

P(Y = 10) = (e^-12 * 12^10) / 10! = 0.1143

(a) Let X be the number of calls received in a 5-minute interval. The arrival rate of calls is 48/60 = 0.8 calls per minute. Then, X follows a Poisson distribution with mean λ = 0.8 * 5 = 4. The probability of receiving two calls in a 5-minute interval is:

P(X = 2) = (e^-4 * 4^2) / 2! = 0.0902

(b) Let Y be the number of calls received in a 15-minute interval. The arrival rate of calls is 48/60 = 0.8 calls per minute. Then, Y follows a Poisson distribution with mean λ = 0.8 * 15 = 12. The probability of receiving exactly 10 calls in 15 minutes is:

P(Y = 10) = (e^-12 * 12^10) / 10! = 0.1143

(c) Let Z be the number of callers waiting after 5 minutes. The arrival rate of calls is 48/60 = 0.8 calls per minute. Then, Z follows a Poisson distribution with mean λ = 0.8 * 5 = 4. The expected number of callers waiting after 5 minutes is:

E(Z) = λ = 4

The probability that none will be waiting is:

P(Z = 0) = e^-4 = 0.0183

(d) Let W be the waiting time until the next call. The time between calls follows an exponential distribution with rate λ = 48/60 = 0.8 calls per minute. Then, the probability that the agent can take 2 minutes for personal time without being interrupted by a call is:

P(W > 2) = e^(-0.8 * 2) = 0.4493

Alternatively, we can use the memoryless property of the exponential distribution to calculate:

P(W > 2) = P(W > 1 + 1) = P(W > 1) * P(W > 1) = e^(-0.8 * 1) * e^(-0.8 * 1) = 0.4493.

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The distance between points A and B is 14 units.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present.

According to the number line,

Point A lie at - 2 on the number line and point B lie at 12 on the number line.

Now from 0 to point B,

The distance between point 0 and B is 12 units.

And from point A to 0 the distance is 2 units.

Therefore,

The total distance between points A and B will be:

AB = AO + OB

AB = 2 units + 12 units

AB = 14 units

Hence, the correct option is (D) 14 units.

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39 subjects were tested in this simple one-way ANOVA.

The df for F distribution is (treatment df, error df)

Using given information

Treatment df = 7

Error df = 31

Total df= 7+31 = 38

Again, total df = N-1, N= number of subjects tested

Then, N-1 = 38

=> N= 39

One-way ANOVA is typically used when there is a single independent variable or factor and the goal is to see whether variation or different levels of that factor have a measurable effect on the dependent variable.

The t-test is a method of determining whether two populations are statistically different from each other, and ANOVA determines whether three or more populations are statistically different from each other.

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The solution of system of equations by Jacobi's method is,

x = 0.4209 ≅ 0.42

y = 0.9471 ≅ 0.95

The given system of equation is,

3.5x - 0.5y = 1

      x - 1.5y = -1

Now apply Jacobi's method to solve this system,

From the above equations

xk+1 = (1/3.5) (1+0.5yk)

yk+1= (1/-1.5) (-1-xk)

Initial gauss (x,y)=(0,0)

Solution steps are

1st Approximation

x1 = (1/3.5) [1+0.5(0)] = 1/3.5 [1] =0.2857

y1 = (1/-1.5)[-1-(0)] = 1/-1.5 [-1] = 0.6667

2nd Approximation

x2 = (1/3.5) [1+0.5(0.6667)] = 1/3.5[1.3333] = 0.381

y2 = (1/-1.5)[-1-(0.2857)] = 1/-1.5 [-1.2857] = 0.8571

3rd Approximation

x3 = (1/3.5)[1+0.5(0.8571)] = (1/3.5)[1.4286] = 0.4082

y3 = (1/-1.5)[-1-(0.381)] = (1/-1.5) [-1.381] = 0.9206

4th Approximation

x4 = (1/3.5)[1+0.5(0.9206)] = 1/3.5[1.4603] = 0.4172

y4 = (1/-1.5)[-1-(0.4082)] = 0.9388

5th Approximation

x5 = (1/3.5)[1+0.5(0.9388)] = 0.4198

y5 = (1/-1.5)[-1-(0.4172)] = 0.9448

6th Approximation

x6 = (1/3.5)[1+0.5(0.9448)] = 0.4207

y6 = (1/-1.5)[-1-(0.4198)] = 0.9466

7th Approximation

x7 = (1/3.5)[1+0.5(0.9466)] = 0.4209

y7 = (1/-1.5)[-1-(0.4207)] = 0.9471

Solution By Gauss Jacobi Method.

x = 0.4209 ≅ 0.42

y = 0.9471 ≅ 0.95

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Answer:

The answer to the question is

2

Step-by-step explanation:

m=8

n=2

=8-3×2

=8-6

=2

Answer:

2

Step-by-step explanation:

ummm

T3(x) = x - x^2/2 + x^3/6.

The Taylor polynomial of degree 3 for the function f(x) = x + e^-x centered at a = 0 is given by:

T3(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3

= 1 + (-1 + 1)x + (e^-0 - (-1)(-1)e^-0)x^2/2! + (0 + (-1)(-1)(-1)e^-0)x^3/3!

= x - x^2/2 + x^3/6

So T3(x) = x - x^2/2 + x^3/6.

An infinite sum of words that are expressed in terms of a function's derivatives at a single point is known as the Taylor series or Taylor expansion of a function in mathematics.

The nth Taylor polynomial of the function is a polynomial of degree n that is created by the partial sum of the first n + 1 terms of a Taylor series. Approximations of a function made by Taylor polynomials get generally better as n rises. Quantitative estimates of the mistake brought about by the use of such approximations are provided by Taylor's theorem. If a function's Taylor series is converging, its total is the upper bound of the Taylor polynomials' infinite sequence. A function's Taylor series sum may not match.

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Answer:

x=2

Step-by-step explanation:

4x+6=x+12

-x         -x

3x+6=12

    -6  -6

3x=6

/3   /3

x=2

Answer:

x=2

Step-by-step explanation:

4x+6 = x+12

Subtract x from each side

4x-x +6 =x-x+12

3x +6 = 12

Subtract 6 from each side

3x+6-6=12-6

3x = 6

Divide each side by 3

3x/3 =6/3

x =2

The man does 960 ft-lb of work against gravity in climbing to the top.

The work done by the man against gravity in climbing to the top can be calculated by finding the change in potential energy. The potential energy is given by the product of the weight and the height.

The weight of the man is 150 lb, and the height he climbs is 160 ft. Therefore, the initial potential energy is 150 lb * 160 ft = 24,000 ft-lb. However, during the ascent, 6 lb of paint leaks out of the can. This reduces the weight that the man carries to 150 lb - 6 lb = 144 lb.

To find the work done against gravity, we need to consider the effective weight of the man (after paint leakage) and the height climbed. The final potential energy is given by the product of the effective weight and the height climbed, which is 144 lb * 160 ft = 23,040 ft-lb.

The work done against gravity is the difference in potential energy, which is the change in potential energy. Therefore, the work done by the man against gravity in climbing to the top is:

24,000 ft-lb - 23,040 ft-lb = 960 ft-lb.

Hence, the man does 960 ft-lb of work against gravity in climbing to the top.

During the calculation, it is important to consider the reduction in weight due to the paint leakage. The effective weight is used to determine the potential energy, which directly affects the work done against gravity. The leakage of paint affects the total weight and, therefore, the potential energy, resulting in a reduction in the overall work done against gravity.

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We will have a Deficit balance of $30 at the end of the month.

"Unilateral transfer" is the term used to describe the balance of payments deficit's most obvious cause. For instance, Americans who contribute money to another country in the form of foreign aid do not receive anything in return (economically speaking). Few economists would argue that foreign aid-related balance of payment deficits are a "bad thing."

Weekly net income = $380

Monthly net income = $380 * 4 weeks = $1520.

Monthly expenses = $1550

Balance = Monthly income - monthly expenses = $-30.

The negative sign shows a deficit of $30 monthly

Therefore, We will have a Deficit balance of $30 at the end of the month.

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Therefore, Two slices of bacon had 96 less calories than three slices of roasted turkey.

a formula that illustrates the connection between two expressions on either side of a sign. It usually only has one variable and an equal sign. like this: 2x – 4 = 2.

Here,

One piece of bacon has 42 calories in it.

There are 60 calories in 1 slice of turkey.

2 slices of bacon are 2 calories each (42)

So 84 calories in 2 slice of bacon

3 slices of roasted turkey have 3 calories each slice (60)

Three slices of roasted turkey have 180 calories each.

180-84 is the difference in the amount of calories.

96 calories are added due to the calorie difference.

Two slices of bacon had 96 less calories than three slices of roasted turkey.

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The equation for the above situation if A store sells gift cards in preset amounts. You can purchase gift cards for ​$20 or ​$30. You have spent ​$560 on gift cards is 2x + 3y = 56.

Equation: A statement stating the equality of two expressions with variables or integers. Since equations are essential questions, attempts to systematically discover the answers to these questions have been the primary motivations for the development of mathematics.

Given:

The price of the gift card = $20 and $30,

Total money spent = $560,

So, the equation will be,

20x + 30y = 560

Here, x is the no of $20 cards and y is the no of $30 cards.

2x + 3y = 56

Therefore, the equation for the above situation if A store sells gift cards in preset amounts. You can purchase gift cards for ​$20 or ​$30. You have spent ​$560 on gift cards is 2x + 3y = 56.

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Answer:

\(y = \frac{-8}{3}x - 8\)

Step-by-step explanation:

Solving for the equation of the line with two points:

Let's remind ourself of the slope - intercept formula:    \(y = mx + b\)

We first have to find the slope of the line. This is found by using the formula :

\(\frac{y_1 - y_2}{x_1 - x_2}\)

We have to find the change in y (Δy) and divide it by the change in x (Δx)

We then have to plug in a coordinate given to us, and use the point's x and y value to find the y - intercept

Let's use the slope formula

\(\frac{0 - (-8)}{-3 - 0} = \frac{8}{-3}\)

Slope = -8/3

To find the y - intercept, we'll update our slope - intercept formula with the slope, and plugin a point. Let's use (-3,0)

\(y = \frac{-8}{3}x + b\)

\(0 = \frac{-8}{3}(-3) + b\)

\(0 = \frac{24}{3} + b\)

\(0 = 8 + b\)

\(b = -8\)

Let's input our slope and y - intercept to the equation     \(y = mx + b\)

Slope = -8/3

Y - Intercept = -8

Equation:    \(y = \frac{-8}{3}x - 8\)

-Chetan K

Answer:

\(1) y = - \frac{3}{2} x + 4\)

\(2)y = x + 5\)

\(3)y = 4 + 5x\)

Answer:

\(The \ equation \ in \ point \ and \ slope \ form \ is; \ y - 3 = -\dfrac{1}{2} \cdot (x - 1)\)

Step-by-step explanation:

The coordinates of the points through which the line passes are (1, 3) and (5, 1)

The slope, m, of a line given the coordinates of two known points on the line, (x₁, y₁), (x₂, y₂) can be found as follows;

\(Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

The slope of the given line is therefore \(m =\dfrac{1-3}{5-1} = \dfrac{-2}{4} = -\dfrac{1}{2}\)

The equation of the line in point and slope form is therefore, y - y₁ = m·(x - x₁) or y - y₂ = m·(x - x₂)

Therefore, by substituting the known values, we have the equation in point and slope form as follows;

\(y - 3 = -\dfrac{1}{2} \cdot (x - 1)\)

Answer:

15cm

Step-by-step explanation:

Theorem: All tangents to a circle from the same point are equal.

Sine E, F, G and H are points of Tangency, by the theorem above:

The diameter line EC divides the Isosceles Trapezoid into two equal parts.

Therefore:

We then have by the equality above that:

BC=BF+FC

=5+10

=15cm

Answer:

b=4

Step-by-step explanation:

3b-4b+3+1=0

-b=-4

b=4

Answer:

1,000 pencils  

Step-by-step explanation:  

First, there are 10,000 cents in $100.  

So divide 10,000 by 10.  

1,000.

I hope this helps!  

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