Kevin ate 2/5 of a pie. Su yung ate 3/10 of the pie. how much of the pie did Kevin and Su Yang eat together

The equations of the lines parallel and perpendicular to the lines f (y = 2), ang g (y = 2·x - 1), with the parallel lines passing through the point P(-2, -1), and the perpendicular line passing through the point Q(3, -2) are;

A. The equation of the line parallel to the line f and passing through the point P is; y = -1

B. Equation of the parallel line to g and passing through P is; y = 2·x + 3

C. Equation of the line perpendicular to f passing through P is; x = 3

D. The equation of the line perpendicular to g and which passes through P is y = -0.5·x - 0.5

Perpendicular lines are lines that intersect forming (right angles) an angle of 90°.

The equation that represents the line f is y = 2

The equation that represents the line y = 2·x - 1

A. The slope of a line parallel to another line are the same, therefore;

The equation of the line parallel to the line y = 2, has a slope which is the coefficient of x of 0.

The line f is parallel to the x-axis

The equation that is parallel to line f and passes through the point P(-2, -1)  therefore has the same y-value as the point P of -1 and an x-value of 0, the equation is therefore;

B. The slope of the line g, y = 2·x - 1 is 2

The slope of the graph of the equation of the line that is parallel to the line g, is also 2

The equation of the line parallel to the line g and passing through the point (-2, -1) is; y - (-1) = 2·(x - (-2)) = 2·x + 4

y + 1 = 2·x + 4

y = 2·x + 4 - 1 = 2·x + 3

The equation of the line parallel to the line g and passing through the point P(-2, -1) is therefore;

C. The line f is parallel to the x-axis, therefore, the line perpendicular to the line f is perpendicular to the x-axis or parallel to the y-axis

The equation of the line perpendicular to the line f and passing through the point Q(3, -2), is therefore;

D. The slope of the line perpendicular to the line g, has a slope that is the negative inverse of the slope of the line g

The slope of the line g is 2, therefore, the slope of the perpendicular line is -1/2

The equation of the perpendicular line to the line of the equation g and passing through the point Q(3, -2) in point-slope form is therefore;

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

y = -x/2 + 3/2 - 2 = -x/2 - 1/2 = -0.5·x - 0.5

y = -0.5·x - 0.5

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The solution of the given greatest integer function is found as 3.5.

We have to compute;

f(x) = 1/2[x]

Given what we have; f(7.6).

Enter x = 7.6 in the function provided;

f(7.6) = 1/2[7.6]

As ,the value (7.6) --> 7.0 (greatest integer function)

f(7.6) = 7/2

f(7.6) =  7/2

f(7.6) = 3.5

Thus, the solution of the given greatest integer function is found as 3.5.

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The correct question is-

If f(x) = 1/2[x], what is f(7.6)?

3

3.5

3.8

4

The given rational number 1/4 in the decimal form is 0.25 which is to the nearest thousandths.

We shall represent this as 1.5 pizzas in decimal form.

In this case, the dot stands in for the decimal point, the number before the dot, in this case, "1," represents one entire pizza, and the number after the decimal point, or the fractional component, represents the other half of the pizza.

So, we have the rational number:

1/4

Convert to decimal as follows:

1/4 = 0.25

Rounding off to the nearest thousandth: 0.2500 ⇒ 0.25

Therefore, the given rational number 1/4 in the decimal form is 0.25 which is to the nearest thousandths.

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Matrix multiplication, also known as matrix product and the multiplication of two matrices, produces a single matrix. It is a type of binary operation. If A and B are the two matrices, then the product of the two matrices A and B are denoted by: X = AB.

The multiplication is done by adding the elements obtained by multiplying each element of the lines of the first matrix times the elements of the columns of the second matrix (Line× Column).

[tex]A=\left[\begin{array}{ccc}1&2\\\end{array}\right] _{1*2} \\B= \left[\begin{array}{ccc}4&5&6\\7&8&9\end{array}\right] _{2*3}[/tex]

2=2 yes it is possible to multiply

1*3= order of the resulting matrix

(line*column)

[tex]A*B=\left[\begin{array}{ccc}4+14&5+16&6+18\\\end{array}\right] _{1*3}[/tex]

[tex]A*B=\left[\begin{array}{ccc}18&21&24\\\end{array}\right] _{1*3}[/tex]

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Answer:

(1, -1)

Step-by-step explanation:

we isolate y in the first equation

2x+y=1

-2x.  -2x

y=1-2x

and now we fill y into second equation

4x-2(1-2x)=6

4x-2+4x=6

8x-2=6

   +2 +2

8x=8

/8 /8

x=1

and now to find y we insert x

2(1)+y=1

2+y=1

-2.   -2

y= -1

hopes this helps

The angle between the ladder and the ground is - 0.075 rad/s.

Pythagoras' theorem is a essential relation in Euclidean geometry among the 3 facets of a proper triangle. It states that the region of the rectangular whose aspect is the hypotenuse (the aspect contrary the proper angle) is identical to the sum of the regions of the squares on the alternative  facets.

cosθ = x/10

On differentiating the above equation,

- sinθdθ/dt = (1/10)dx/dt

dθ/dt = -(1/10)dx/dt/sinθ

sinθ = y/10

= √(100 - 36)/10

= 0.8; dθ/dt

= -(1/10)·0.6 ft/s/0.8

= - 0.075 rad/s

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The amount of money with Adam and Braulio as per given system of equations is equal to $84 and $69.

As given in the question,

Let 'a' be the amount of money with Adam

And 'b' be the amount of money with Braulio

System of equations as per given given data:

b = a - 15___(1)

a + b = 153 ___(2)

Substitute the value of 'b' in (2) we get,

a + a -15 = 153

⇒2a = 153 + 15

⇒2a = 168

⇒ a = $84

Amount of money with Adam is $84

Amount of money with Braulio is b = 84 - 15

                                                          = $69

Therefore, the amount of money with Adam and Braulio is equal to $84 and $69.

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Answer:

1/4

Step-by-step explanation:

4 : 1 = 1 : x

x = 1 · 1 / 4

x = 1/4

If the exterior angle is of 90º, it's adjacent interior angle will also be of 90º

What is exterior angle property of triangle?

According to the exterior angle theorem, the exterior angle that results from stretching a triangle's side is equal to the sum of the dimensions of the triangle's two opposed interior angles. The theorem can be used to determine a triangle's unknown angle's measurement. We must first determine the triangle's exterior angle and then its two remote inner angles in order to apply the theorem.

Using the concept of supplementary angles, it is found that the measure of an exterior angle of a triangle is equal to the measure of it's adjacent interior angle if both measure 90º.

Two angles are called supplementary if their measures add to 180º.

The exterior angle of a triangle is supplementary to it's adjacent interior angle.

Thus, if the exterior angle is of 90º, it's adjacent interior angle will also be of 90º.

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Answer: 7

Step-by-step explanation:

We substitute n for 14 to get the equation 14-7, which equals 7.

A triangle whose sides are all equal is called an equilateral triangle and its area is given by A=[tex]\frac{\sqrt{3} }{4}[/tex] [tex]x^{2}[/tex], where x is the side of the triangle.

The area of a rectangle is found by using the formula

A=lw, where l is the length and w is the width.

The given figure can be split into two shapes: a rectangle and an equilateral triangle as shown in the diagram. Let l be the length of the rectangle.

Add all of the sides of the window and equate their result to 16. Then solve for l.

x + x + l + x + l = 16

3x + 2l = 16

2l = 16 - 3x

l = [tex]\frac{16-3x}{2}[/tex]

The total area of the window will be the sum of the area of the equilateral triangle ABE and the area of rectangle BCDE.

A = [tex]\frac{\sqrt{3} }{4}[/tex][tex]x^{2}[/tex] + lx

Subsitute  [tex]\frac{16-3x}{2}[/tex] for l into the obtained equation and simplify.

A =[tex]\frac{\sqrt{3} }{4}[/tex][tex]x^{2}[/tex] + ( [tex]\frac{16-3x}{2}[/tex])x

A = [tex]\frac{\sqrt{3} }{4} x^{2}[/tex] + 8x - [tex]\frac{3}{2} x^{2}[/tex]

Differentiate the obtained equation with respect to x and equate the first derivative to 0 to calculate the critical point x .

[tex]\frac{dA}{dx}[/tex] = [tex]\frac{\sqrt{3} }{4}[/tex] (2x) + 8 - [tex]\frac{3}{2}[/tex] (2x)

0 = [tex]\frac{\sqrt{3} }{2}[/tex] x - 3x + 8

x (3 - [tex]\frac{\sqrt{3} }{2}[/tex]) = 8

x = [tex]\frac{16}{6-\sqrt{3} }[/tex]≈3.74887

Again, differentiate the equation

[tex]\frac{dA}{dx}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex]x - 3x + 8  with respect to x.

[tex]\frac{d^{2}A }{dx^{2} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] - 3

The value of the second derivative is [tex]\frac{\sqrt{3} }{2}[/tex]−3, which is negative. This implies that the area will be maximum at the critical point.

Subsitute x = 3.74887 into the equation

l = [tex]\frac{16-3x}{2}[/tex] and simplify

l = [tex]\frac{16-(3)(.74887)}{2}[/tex] ≈ 2.3767

The maximum light will enter through the window when the triangular portion will have the side length of 3.74887 feet and the dimensions of the rectangular portion will be 3.74887-ft-by-2.3767-ft.

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Answer:10

Step-by-step explanation:

Answer:

$37.50

Step-by-step explanation:

75% of $50:

0.75x50=$37.50

The equation of the circle in general form is x² + y² - 2 · x - 2 · y - 8 = 0.

In this problem we need to derive the equation of a circle that contains three points: (x₁, y₁) = (- 2, 2), (x₂, y₂) = (2, 4), (x₃, y₃) = (4, 0). The general form of the equation of the circle is a second order polynomial of the form:

x² + y² + B · x + C · y + D = 0

Where B, C, D are real coefficients.

First, use the points to generate a system of linear equations:

- 2 · B + 2 · C + D = - 8

2 · B + 4 · C + D = - 20

4 · B + D = - 16

Second, resolve the system by means of numerical methods:

(B, C, D) = (- 2, - 2, - 8)

Third, write the general form of the equation is:

x² + y² - 2 · x - 2 · y - 8 = 0

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Answer:

Step-by-step explanation:

?

The component that is missing from the biologist's process is: c. The biologist did not randomly assign the each of the bats to the treatment groups.

When we carry out a research study that has  created groups that you want to study, then the differences between and within groups can be thoroughly checked to make sure that they are not systematic when subjects are randomly assigned to groups.

Therefore this random assignment of subjects, gives the researcher the confidence that groups are the same in terms of variables, and any differences can be confidently allocated to experimental treatments.

Therefore, we can conclude that the component that is missing from the biologist's process is given in option C because the biologist did not randomly assign the each of the bats to the treatment groups.

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The distance between the two lines from the graph is 1 unit.

To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.

The given equations are as below,

y = x - 1

And,

y = 2x - 4

They can be drawn on a graph as follows,

From the graph the distance between two lines can be calculated as the difference between their x-intercepts as,

2 - 1 = 1 unit.

Hence, the distance between the two lines is given as 1 unit.

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In the collection, there are 11 nickels and 23 dimes. If each nickel is replaced with a quarter, the value of the collection becomes $5.05. So, C is correct. By writing them in the system of equations, we get the required value.

The given units are nickels, dimes, and quarters. Their conversion into dollars is as follows:

1 nickel = $0.05

1 dime = $0.10

1 quarter = $0.25

Given a collection of nickels and dimes is worth $2.85.

And there are 34 coins in the collection.

So, consider the number of nickel coins = n and the number of dime coins = d.

Then, the equation for the given collection is

n + d = 34...(1)

0.05n + 0.10d = 2.85...(2)

On simplifying (2), we get

5n + 10d = 2.85 × 100

⇒ 5n + 10d = 285

From (1), n = 34 - d, we get

5(34 - d) + 10d = 285

⇒ 170 - 5d + 10d = 285

⇒ 5d = 285 - 170 = 115

∴ d = 115/5 = 23

Thus, the number of dime coins is 23.

So, from (1), we get n + 23 = 34 ⇒ n = 34 - 23 = 11

∴ n = 11

Thus, the number of nickel coins is 11.

If each nickel coin in the collection is replaced with a quarter, then the value of the collection is

q + d = 34 and 0.25q + 0.10d = Y

Here q = 11; d = 23

So, we get

0.25(11) + 0.10(23) = Y

⇒ 2.75 + 2.3 = Y

⇒ 5.05 = Y

∴ Y = $5.05

The value of the new collection becomes $5.05.

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The probability that Lamar and Lawrence finish their jobs within 5 minutes of each other on a randomly selected day is 0.2892

Consider the time for the Lamar to finish the job as x and the time for the Lawrence to finish the job as x

Consider the random variable x-y

x-y normal with mean = 105 - 98

= 7

Similarly the variance of the random variable x-y

= 105 + 225

= 325

The standard deviation = [tex]\sqrt{325}[/tex]

= 18.03

Here we have to find the probability that Lamar and Lawrence  finish their jobs within 5 minutes of each other on a randomly selected day

P(|x-y|<5) = P(-5<U<5)

Now we have to convert to standard normal variate Z

Then the it will be

(-5-7)/18.03 = -0.67

(5-7) / (18.03)= 0.11

The probability of the given condition will be

P(-0.67<Z<0.11) = 0.2454 + 0.0438

Add the terms

= 0.2892

Therefore, the probability is 0.2892

The complete question is:

Lamar and Lawrence run a two-person lawn-care service. they have been caring for Mr. Johnson's very large lawn for several years, and they have found that the time it takes Lamar to mow the lawn itself is approximately normally distributed with a mean of 105 minutes and a standard deviation of 10 minutes. meanwhile, the time it takes for Lawrence to use the edger and string trimmer to attend to details is also normally distributed with a mean of 98 minutes and a standard deviation of 15 minutes. they prefer to finish their jobs within 5 minutes of each other. what is the probability that this happens, assuming their finish times are independent?

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The value of SSE (sum squared error) is 40 in the given analysis of the variance problem if SST = 120 and SSR = 80. Option b is correct.

Here the words SSE means Sum Squared Error, SST means Sum of Squares Total and SSR means Sum of Square Regression.

In the SSE accuracy measure, errors are squared and then added. It is used when the data points are similar in magnitude.

The formula is SST = SSR + SSE ⇒ SSE = SST - SSR

The given values of the analysis of the variance problem are

SST = 120; SSR = 80

Then, the value of SSE = SST - SSR = 120 - 80 = 40

So, option b is correct.

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The Sum of the first six terms of the progression is 14706

What is Geometric Progression?

A geometric progression, also known as a geometric sequence, is a non-zero numerical series in which each term after the first is determined by multiplying the preceding one by a fixed, non-zero value known as the common ratio.

Solution:

On carefully observing

We can state that, the Common Ratio is -7

Sum(n) = a([tex]r^{n}[/tex] - 1) / r - 1

Sum(6) = -1 (-7^6 - 1) / -7-1

Sum(6) = -1(117648)/-8

Sum(6) = 14706

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Answer:

[tex]r=-\frac{\sqrt{7}}{7} \implies p=\sqrt{7}[/tex]

Step-by-step explanation:

We know that [tex]pr=-1[/tex] and [tex]p=49|r|[/tex].

[tex]\frac{-1}{r}=49|r| \\ \\ \frac{1}{r^2}=49r^2 \\ \\ 1=49r^4 \\ \\ r^4=\frac{1}{49} \\ \\ r=-\frac{\sqrt{7}}{7} \implies p=\sqrt{7}[/tex]

Answer:

Yes, there is. It's called a regular 52-gon.

Answer:

$22.55

Step-by-step explanation:

Not 100% sure but you can double check...

Unit rate is the quantity of an amount of something at a rate of one of another quantity.

The fewest number of hours he would need to work to reach his goal of $280 is 28 hours working in the library.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

Amount to earn = $280

Grocery store:

Earnings per hour = $8

1 hour = $8

Multiply 280/8 on both sides.

280/8 x 1 hour = $280

35 hours = $280

Library:

Earnings per hour = $10

1 hour = $10

Multiply 280/10 on both sides.

28 hours = $280

We see that,

Working in the Library would make $280 in fewer hours than working in the grocery store.

Thus,

The fewest number of hours he would need to work to reach his goal of $280 is 28 hours working in the library.

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The height of the stone before it is dropped is 4.64 feet, and the time taken to hit the ground is 3.94 seconds.

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

Given:

The function y =  - 16t² + 248

Calculate the value of t when f(t) = 0.

0 = -16t² + 248

t² = = 248 / 16 = 15.5

t = √15.5 ≈ 3.94  Seconds

Calculate the height at t = 3.94

y = -16 × 3.9² + 248

y = -243.36 + 248

y = 4.64 feet

Therefore, the height of the stone before it is dropped is 4.64 feet, and the time taken to hit the ground is 3.94 seconds.

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Emma is asking an empirical question so that she she can test her hypothesis

What is a Empirical hypothesis?

Something empirical is something based on real evidence .

Evidence that is verifiable by observation as opposed to something that is true in theory or by some kind of reckoning or logic

A hypothesis is a theory that is put forward for further examination to see if it is correct. It is not a call but it is an explanation that fits the available evidence so , An empirical hypothesis is a theory that is based on real evidence and experience but that has not been proven yet

So, According to the question

Emma wants to know if long distance relationship in college have a greater likelihood of ending than a relationship that are not long distance and for that she creates a questionnaire and the crowds 100 student from our school to complete the questionnaire so she can test her hypothesis

Here, Emma is asking an empirical questions ( question about experience) and will conclude the test based on these 100 students experience and thoughts.

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The binomial series is used to expand a binomial expression of the form (a + b)^n, where 'a' and 'b' are constants and 'n' is a positive integer. In this case, we are expanding (1-x)^1/3.

Step 1: Rewrite the expression using the binomial theorem. We can rewrite (1-x)^1/3 as (1 + (-x))^1/3.

Step 2: Use the binomial theorem to expand the expression.

The binomial theorem states that (a + b)^n

= nC0*a^n + nC1*a^(n-1)*b + nC2*a^(n-2)*b^2 + ... + nCn*b^n.

Since 'n' is a 1/3 in this case, we can rewrite the expression as

(1 + (-x))^1/3

= 1C0*1^1/3 + 1C1*1^(1/3-1)*(-x) + 1C2*1^(1/3-2)*(-x)^2 + ...

Step 3: Substitute the values. We can substitute the values into the expression to get (1 + (-x))^1/3

= 1 + (-x) + (-x)^2 + ...

Step 4: Simplify the expression. The expression simplifies to

(1 - x + x^2 - x^3 + ...).

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There is no sufficient evidence to support the claim that there is a difference in the longevity of the two brands of batteries , as the null hypothesis failed to be rejected.

So the mean and standard deviation for the sample of battery 1 is :

M(1)=  106+ 111+ 109+ 105/4 =107.75

standard deviation (1)=r√(x(i)-M/(n-1)=root(22.75/3)=2.754

Similarly, for the second  battery, the mean and   standard deviation  is

M(2)= 125 +103+ 121+ 118/4=116.75

S(2)=√(276.75/3)=√(92.25)=9.605

Here the hypothesis test for the difference between populations means, here the claim is that the longevity of the two brands of batteries differs.So the alternative and null hypotheses are:

H(0)= μ1-μ2=0

H(1)=μ1-μ2 ≠0

Here the  significance level is 0.05(α), The difference between sample means is M(d)=107.75- 116.75=-9 .Now the  estimated standard error of the difference between the means is :

s(Md)=√(2.754²+9.605²/4)=4.996, Now the test static will be, t=-9-0/4.996=-1.8014 and the degree of freedom is 4+4-2=6 .Here  the test is two-tailed  with  degrees of freedom of  the test static is -1.8014, so the P-value for the  test is : 2.P(t< -1.8014)=0.122

Here the P-value (0.122) is greater than the significance level so the effect is insignificant, and the null hypothesis failed to be rejected.

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the operations manager of a manufacturer of television remote controls wants to determine which batteries last the longest in his product. he took a random sample of his remote controls and tested two brands of batteries. the number of minutes of continuous use before the batteries failed for each brand is given in battery.xlsx. if the significance level is 10%, is there statistical evidence of a difference in longevity between the two batteries?

The sample data for each battery is:

Battery 1: 106 111 109 105

Battery 2: 125 103 121 118