The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds.

The equation represents the parabola shown on the graph is  x^2 = - 8y . Option D

We were given the following parameters;

The standard for a parabola is given as;

y² = 4ax

It can also be written as;

x² = 4ay

Given the focus as ( -2, 0), we have the value of 'a' to be -2

Now, let's substitute the value into the standard equation of a parabola

x^2 = 4ay

x^2= 4 × -2 × y

Multiply through

x^2 = - 8y

The equation of the parabola is x^2 = - 8y

Thus, the equation represents the parabola shown on the graph is  x^2 = - 8y . Option D

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Answer:

b

Step-by-step explanation:

trust

The cofactors of each entry in the first row of the matrix exist

[tex]$$Ac_{11 }= -13[/tex]

[tex]Ac_{12} = 44[/tex]

[tex]Ac_{13} = 27[/tex]

We have to estimate the cofactors of each entry in the first row of the matrix.

A set of numbers exists arranged in rows and columns to create a rectangular array. The numbers exist named the elements, or entries, of the matrix.

Thus the cofactors of each entry in the first row of the matrix exist

[tex]$$Ac_{11 }= -13[/tex]

[tex]Ac_{12} = 44[/tex]

[tex]Ac_{13} = 27[/tex]

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Answer:

b.  2x^10y^12.

Step-by-step explanation:

(60x^(20)y^(24))/(30x^(10)y^(12)

60 / 30 = 2

x^20 / x^10 = x^(20-10) = x^10

y^(24) / y^(12) = y^(24-12) = y^12.

Thus, the answer is:

2x^10y^12.

Answer:

b. 2x^(10)y^(12)

Step-by-step explanation:

(60x^(20)y^(24))/(30x^(10)y^(12)

when there is division we simplify that by subtracting the power

by using rules of indices

[tex] \frac{x^a}{x^b}=x^{a-b}[/tex]

and number can be divided easily

[tex] \frac{60}{30}*\frac{x^{20}}{x^{10}}*\frac{y^{24}}{y^{12}}[/tex]

[tex] 2*x^{20-10}y^{24-12}[/tex]

[tex] 2x^{10}y^{12}[/tex]

so answer is b. 2x^(10)y^(12)

Answer:

1. 36 liters

2. 3 kg

Step-by-step explanation:

because 12 liters is 4kg if you multiply both by 3 you’ll get that 12 kg is equal to 36 liters

also, if you divide both by 4, you’ll see that 1kg is equal to 3 liters. Then with this knowledge, yiucc be an see that if you multiply both by 3; 3 kg will be 9 liters! :)

Answer:

1.) 36 litres

2.) 3 kg

Step-by-step explanation:

In this case there is a ratio of 1:3 of mass to volume.  If we know the mass, the volume is 3 times that.  If we know the volume, the mass is that divided by 3.

Answer:

12x+6

Step-by-step explanation:

Can i have brainliest

Answer: 12x + 6

Step-by-step explanation:

In Distributive property, you multiply each of the numbers in the parentheses by the outside number.

Universities A had an income under $20,000 25% graduates.

A two way table is a way to display frequencies or relative frequencies for two categorical variables. One category is represented by rows and a second category is represented by columns.

Researchers surveyed recent graduates of two different universities about their income. The following two-way table displays data for the sample of graduates who responded to the survey.

A had an income under $40,000 25% graduates.

We have to add 30 45 together and get 75 because those are the students that have income under $40,000 dollars in both Universities

Then u convert have to convert it to a percentage and get 25%.

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The above question is not complete:

Researchers surveyed recent graduates of two different universities about their income. The following two-way table displays data for the sample of graduates who responded to the survey.

How many graduates from University A had an income under $40,000?

________graduates.

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The answer is 25%

its what khan says :>

The area of the baseball diamond is 8192 sq. units.

We assume the square-shaped, baseball diamond to be ABCD with A = (0, 64), B = (64, 0), C = (0, -64), and D = (-64, 0).

The side of the square can be computed using the distance formula,

D = √((x₂ - x₁)² + (y₂ - y₁)²), when the endpoints of a line are (x₁, y₁) and (x₂, y₂).

Thus, the side of the square,

a = √((x₂ - x₁)² + (y₂ - y₁)²),

or, a = √((64 - 0)² + (0 - 64)²) {Considering A(0,64) and B(64, 0) as the endpoints,

or, a = √(64² + (-64)²),

or, a = √(4096 + 4096),

or, a = 64√2 units.

Now, the area of the square can be calculated using the formula, A = a², where A is the area and a is the side of the square.

Thus, the area of the square = (64√2)² = 4096*2 = 8192 sq. units.

Thus, the area of the baseball diamond is 8192 sq. units.

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Answer:

34 L

Step-by-step explanation:

there are four 100 km(s) in 400 km

so

8.5 * 4 is what you need to do to find your answer

8.5 * 4 = 34

34 L is your answer

Answer:

A = 0; B = -9/2

Step-by-step explanation:

To have no solutions, you need parallel lines with equal slopes and different y-intercepts.

3x + 4y = A      Eq. 1

Bx - 6y = 15     Eq. 2

In Eq. 1, notice that the coefficient of x is 3/4 of the coefficient of y.

We must have the same ratio for the coefficients in Eq. 2.

B/(-6) = 3/4

4B = -6(3)

4B = -18

B = -9/2

Now we have

3x + 4y = A      Eq. 1

-9/2 x - 6y = 15     Eq. 2

How do we change the left side of the second equation into the left side of the first equation? -6/4 = -3/2 and also -9/2 ÷ 3 = -3/2

To change the left side of the second equation into the left side of the first equation, divide the left side by -3/2.

If we divide 15 by -3/2 we get -10.

The equation -9/2 x - 6y = -10 is the same as Eq. 1, so that would create a system of equations with only one equation and an infinite number of answers.

To have no equations, the y-intercepts must be different, so A can be any number other that -10.

Answer: A = 0; B = -9/2

The required minimum sample size to construct a 95% confidence level for the population mean is 267.

In this question,

In the probability and statistics theory, the confidence interval of the population parameter is the estimated range of values we are sure with a certainty that our parameter will lie within, the range being calculated from the sample obtained. The smaller is the margin of error, the more confidence we have in our results.

The population standard deviation, σ = 25

Confidence level for the population mean = 95%

Margin of error = ±3

Let n be the sample size of the population

The z-score for the confidence level of 95% for the population mean is 1.96.

The formula of margin of error is

[tex]E=\frac{z \sigma}{\sqrt{n} }[/tex]

Now, the sample size of the population can be calculated as

[tex]n=(\frac{z\sigma}{E} )^{2}[/tex]

On substituting the above values,

⇒ [tex]n=(\frac{(1.96)(25)}{3} )^{2}[/tex]

⇒ [tex]n=(\frac{49}{3}) ^{2}[/tex]

⇒ [tex]n=(16.33)^{2}[/tex]

⇒ n = 266.77 ≈ 267

Hence we can conclude that the required minimum sample size to construct a 95% confidence level for the population mean is 267.

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The rate at which battery charges is 10 percent per minute.

According to the statement

we have given that the charging capacity of battery in the graphical representation.

And we from this we have to find the percentage by which battery charges.

And the graphical representation given is :

The horizontal axis is from zero to thirty-two-point-five with a scale of two point five and is titled Time in minutes. The vertical axis is from zero to one hundred with a scale of five and is titled Capacity, percent charged. The graph of the line is y equals two x plus forty. The graph ends at thirty minutes.

A first quadrant coordinate plane. The horizontal axis is from zero to thirty-two-point-five with a scale of two point five and is titled Time in minutes.

And according to this representation it is clear that the percentage by which battery charges is 10 percentage per minute.

So, The rate at which battery charges is 10 percent per minute.

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Answer:

-2n+15>3

Step-by-step explanation:

Using the continuity concept, since the lateral limits and the numeric value of the function are equal at the point in which the definition changes, the function is continuous.

A function f(x) is continuous at x = a if it is defined at x = a, and:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

The definition of the piecewise function is given by:

Since the definition of the function changes at x = 2, and the domain of the function has no restrictions, this is the only point in which there may be a discontinuity.

The lateral limits are:

The numeric value is:

f(2) = 1.5 x 2 = 3.

Since the lateral limits and the numeric value of the function are equal at the point in which the definition changes, the function is continuous.

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We know that there are (3 + 1/2) groups, such that each group fill one bus.

2/5 of the students are boys, then the number of groups that we can make only with boys is:

(2/5)*(3 + 1/2) = 6/5 + 1/5 = 7/5 = 5/5 + 2/5 = 1 + 2/5

Then you can make one and a little less than a half of a group, which means that you need 1 and 2/5 of a buss to transport the boys, rounding that to the a whole number, you will need 2 busses to only transport the boys.

The original distance is:

D = (2 + 3/4) miles.

But Mark only covers 2/3 of that distance, then we have:

d = (2/3)*D = (2/3)*(2 + 3/4) miles = (4/3 + 2/4) miles

d = (4/3 + 1/2) miles = (8/6 + 3/6) miles = (1 + 5/6) miles

Mark is at (1 + 5/6) miles of his house.

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The equation of the line is y = 2/3x + 4

The points on the line are given as:

(zero, four) and (negative six, zero).

Rewrite the points properly as

(0, 4) and (-6, 0)

The slope of the line is calculated using:

m =(y2 - y1)/(x2 - x1)

Substitute the known values in the above equation

m = (0 - 4)/(-6 - 0)

Evaluate

m = 2/3

The equation of the line is then calculated as:

y = mx + b

This gives

y = 2/3x + b

So, we have:

4 = 2/3 * 0 + b

Evaluate

b = 4

Substitute b = 4 in y = 2/3x + b

y = 2/3x + 4

Hence, the equation of the line is y = 2/3x + 4

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The three parts weigh 27/112 pound ( letter B).

The question gives:

Therefore, each part will be  [tex]\frac{\frac{9}{16} }{7} =\frac{9}{16} *\frac{1}{7} =\frac{9}{112}[/tex].

For knowing the three parts weigh, you should mulitiply the previous value for 3. Thus,

[tex]\frac{9}{112}*3=\frac{27}{112}[/tex].

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The weight of three parts is 27/112 pounds

The weight of the chocolate bar is given as:

Weight = 9/16

When it is cut into 7 equal parts, the weight of each part is

Each = Weight/7

This gives

Each = 9/16 * 1/7

Evaluate the product

Each = 9/112

The weight of three parts is then calculated as:

Three parts = Each * 3

This gives

Three parts = 9/112 * 3

Evaluate the product

Three parts = 27/112

Hence, the weight of three parts is 27/112 pounds

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Answer:

3.71

Step-by-step explanation:

The mean absolute deviation(MAD) of a data set is given by the formula

[tex]$ MAD =\frac{1}{n} \sum_{i=1}^n |x_i-\bar{x}|$[/tex]

[tex]n[/tex] = number of data set values. Here [tex]n = 7[/tex]

[tex]\bar{x}=[/tex] mean of the data set values; [tex]\bar{x}=[/tex] [tex](14+13+16+12+17+21+26)/7[/tex] = [tex]119/7=17[/tex]

[tex]x_{i}[/tex] are the n individual values

[tex]\frac{1}{7} |14-17| + |13-17| + |16-17| + |12-17| + |17-17| + |21-17| + |26-17|\\= (3 + 4 + 5 + 1+ 0 + 4 + 9)/7\\= 26/7 = 3.71428 \\[/tex]

= [tex]3.71 \textrm{ rounded to the nearest hundredth}[/tex]  Answer  

Answer:

1/2.x+3(x-1)-5=30

1/2.x+3x-3-5=30

(1/2+3)x-8=30

7/2.x-8=30

7/2.x=38

7x=76

x=76/7

CMIIW

1. The 100 prisoner experiment: 100 prisoners are about to be executed (you can use paper stick figures to model 100 prisoners, or you can do about 10), but the warden has agreed to allow all prisoners to be commuted to a 6-month sentence if they can pass one game. The game states that 100 pieces of paper with each of the prisoner's numbers are to be randomly shuffled into boxes that have random prisoner's numbers (where the number on the paper does not match the number on the boxes.) Each prisoner is allowed to open 50 boxes to find their number such that they have a [tex]\frac{1}{2}[/tex] chance of finding their number. If you find your number, you are cleared to another room to wait. If you don't, then you've messed up huge. If even one prisoner does not find their number, all the prisoners die. If all of the prisoners find their numbers, they all get 6-month sentences instead. The chance of all the prisoners randomly finding their numbers is [tex](\frac{1}{2})^{100}[/tex], which is about a 0.0000000000000000000000000000008% chance. 30 zeros after the decimal placement. For reference, two people have a better chance of picking up the same grain of sand from any of the beaches in the world than finding their numbers randomly.

The Vickrey Auction can be modeled into an experiment by testing people's psychological thinking. You can do this with any of your friends. In a Vickrey auction, you put your bids into a closed letter. For an item, the highest bidder wins the auction, but does not pay what he or she put their bid under in the auction, but rather pays what the second bidder had bidded. It teaches people to be more honest, because if you bid the highest and win, you pay the second-highest bidder's payment, which could also be almost equally as high and could cost you a fortune for an undervalued item.

Another great experiment you can do is to measure the different unsynchronizations of analog clocks that are not close together. Scientists have measured atomic clocks that are just a millimeter apart that start ticking in different measures.

2. I select the 100-prisoner experiment.

3. A curved graph like -x^2 would fit perfectly.

4. A quadratic function would fit my experiment the best. The best graph to use would be [tex]y = -x^2[/tex]. An equation with a large curve would be the best for this type of experiment to graph success and failure. More than three quarters of my graph wouls be full of failure and maybe a little more than 10% would be full of success if repeated over 100,000 times. I am not too sure though.

Answer:

-(-3) ± √(-3)^2 - 4(2)(-5) / 2(2)  (the last choice).

Step-by-step explanation:

Im ignoring the 2^2 in the equation

The equation transforms to

2x^2 - 3x - 5 = 0    (standard form)

So x = -(-3) ± √(-3)^2 - 4(2)(-5) / 2(2)

The function to represent the problem is f(x)=6x+24 and the range is 30[tex]\leq[/tex]y[tex]\leq[/tex]48.

If the terms of a sequence differ by a constant, we say the sequence is arithmetic. If the initial term ([tex]a_{0}[/tex]) of the sequence is a and the common difference is d, then we have,

[tex]a_{n}[/tex]=a+(n-1)d

Initial number of clients=30

Number increase per week= 6

So, we can make an arithmetic sequence fir six weeks

30,36,42,48

Here, first term, a=30

Common difference, d=6

Range is [30,48]

The explicit formula of an arithmetic sequence is

[tex]a_{n}[/tex]=a+(n-1)d

Put a=30, d=6, n=x

[tex]a_{x}[/tex]=30+(x-1)6

[tex]a_{x}[/tex]=30+6x-6

[tex]a_{x}[/tex]=6x+24

Therefore, The function to represent the problem is f(x)=6x+24 and the range is 30<=y<=48

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The graph that shows the solutions for the inequality, y > -1/3x + 1 is: C. Graph A.

The inequality sign, ">" means that the graph of the inequality has a dashed line where the shaded part is above the boundary line and the boundary line is dashed or dotted. If "≥" is used, the boundary line would not be dashed or dotted and the shaded area would be above it.

On the other hand, "<" is used when the shaded area is below the boundary line and the boundary line is a dashed line. If "≤" was used, the boundary line won't be dashed or dotted, while the shaded area would be below the boundary line that is not dotted.

Given y > -1/3x + 1, the slope (m) = change in y / change in x is -1/3.

Graph A has a slope of -1/3 and the shaded part is above the boundary line.

Therefore, the graph that shows the solutions for y > -1/3x + 1 is: C. Graph A.

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Answer:

76

Step-by-step explanation:

In order for John's average to be 80, the sum of all of his test scores must be 4*80 = 320. We can add 84, 78, and 82 to get 244, and then we subtract 244 from 320 to obtain the answer 76.

Answer:

Step-by-step explanation:

80 * 4 = 320

84 + 78 + 82 + x = 244

244 + x = 320

x = 320 - 244

x = 76

Answer: 12 cm

Step-by-step explanation:

[tex]\mathtt{Using\ the \ pythagorean \ theorem: \\}[/tex]

[tex]a^2+b^2=c^2, \\\ we\ can\ plug\ in\ values\ for\ a,\ b,\ and\ c[/tex]

[tex]L=a\ and\ M=b\ and\ N=c[/tex]

Therefore,

[tex]L^2+35^2=37^2\\L^2+1225=1369\\L^2=144\\\sqrt{L^2} =\sqrt{144} \\L=\pm12\\Taking\ only\ the\ positive\ answer,\ we\ get:\\\large\boxed{L = 12cm}[/tex]

We have: L² + M² = N²

=> L² = N² - M² = 37² - 35² = 144 = 12²

=> L = 12

ANSWER: B.12

OK done. Thank to me :3

The logarithmic equation f(x) = log₈(x + 1) + 4 is shifted left by 1 unit and up by 4 units

The logarithmic equation is given as:

f(x) = log₈(x + 1) + 4

The parent function of the logarithmic equation is

y = log₈(x)

When the logarithmic equation is translated 1 unit left, we have:

y = log₈(x + 1)

When the logarithmic equation is translated 4 units up, we have:

y = log₈(x + 1) + 4

This means that the logarithmic equation f(x) = log₈(x + 1) + 4 is shifted left by 1 unit and up by 4 units

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The power series for given function [tex]g(x)=\frac{4x}{(x-1)(x+3)}[/tex] is [tex]g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex]

For given question,

We have been given a function g(x) = 4x / (x² + 2x - 3)

We need to find a power series for the function, centered at c, for c = 0.

First we factorize the denominator of function g(x), we have:

[tex]\Rightarrow g(x)=\frac{4x}{(x-1)(x+3)}[/tex]

We can write g(x) as,

[tex]\Rightarrow g(x)=\frac{1}{x-1}+\frac{3}{x+3}\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1+\frac{x}{3} }\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1-(-\frac{x}{3} )}\\[/tex]

We know that, [tex]\frac{1}{1-x}=\sum{_{n=0}^\infty}~{x^n}[/tex] if |x| < 1

and [tex]\frac{1}{1-(-\frac{x}{3} )}=\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n[/tex]  if [tex]|\frac{x}{6}| < 1[/tex]

[tex]\Rightarrow g(x)=-\sum{_{n=0}^\infty}~x^n+\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n\\[/tex]     if |x| < 1 and  if [tex]|\frac{x}{6}| < 1[/tex]

[tex]\Rightarrow g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex] if |x| < 1

Therefore, the power series for given function [tex]g(x)=\frac{4x}{(x-1)(x+3)}[/tex] is [tex]g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex]

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Applying the angle bisector and triangle proportionality theorem, the solutions are:

16. x = 1/2 or x = 4

17. x = 5

18. x = −1 or x = 6.

The angle bisector theorem states that when a line segment divides one of the angles of a triangle into two halves, it also divides the triangle to form segments that are proportional to each other.

16. 3x/(x - 1) = (x + 4)/(x - 2) [triangle proportionality theorem]

Cross multiply

(x - 1)(x + 4) = 3x(x - 2)

x² + 3x - 4 = 3x² - 6x

x² - 3x² + 3x - 4 + 6x = 0

-2x² + 9x - 4 = 0

Factorize -2x² + 9x - 4

(−2x + 1)(x − 4)

-2x = -1

x = 1/2

or

x = 4

17. (2x + 2)/(x + 3) = (4x - 2)/(2x + 2)

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

4x² + 8x + 4 = 4x² + 10x - 6

Combine like terms

4x² - 4x² + 8x - 10x = -4 - 6

-2x = -10

x = -10/-2

x = 5

18. (2x + 3)/(x + 4) = x/(x - 2) [angle bisector theorem]

Cross multiply

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

Expand

2x² - x - 6 = x² + 4x

2x² - x - 6 - x² - 4x = 0

x² - 5x - 6 = 0

Factorize x² - 5x - 6 = 0

(x+1)(x−6) = 0

x = −1 or x = 6

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Correct option is D) and E)

(3,7π/6),(3,11π/6)

Point of intersection is the point where two lines or two curves meet each other.

The point of intersection of two lines of two curves is a point.

If two planes meet each other then the point of intersection is a line.

The term "point of intersection" refers to the intersection of two lines. The equations a1x+b1y+c1=0 and a2x+b2y+c2=0, respectively, are used to represent these two lines. The two lines' intersection point is shown in the following figure. The intersection of three or more lines can also be located.

let

5 + 4 sin(θ) = −6 sin(θ)

Then get

θ= -1/2

Then you can make it

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I understand that the question you are looking for is:

On the interval [0, 2π), which points are intersections of r = 5 4 sin(θ) and r = −6 sin(θ)? check all that apply.

A) -3,7/6

B) (-3,11/6)

C) (3,7/6)

D) (3,11/6)

Answer:

Step-by-step explanation:

[tex]We\ summarize\ (1) \ and\ (2),\ \ (2) \ and\ (3):\\\displaystyle\\\left \{ {{2x\geq -6\ |:2} \atop {-2x\geq -6\ |:(-2)}} \right. \ \ \ \ \ \left \{ {{x\geq -3} \atop {x\leq 3}} \right. \ \ \ \ \ \Rightarrow\ \ \ \ x\in[-3;3].\\[/tex]

[tex]2)\ We\ subtract\ equation\ (2) \ from \ equation (1),[/tex]