x 2.6.PS-13


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You use a garden hose to fill a wading pool. If the water level rises 17 centimeters every 5 minutes


and you record the data point of (15,y), what is the value of y? Use slope to justify your answer.

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 2250\\ P=\textit{original amount deposited}\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &17 \end{cases}\)

\(2250 = P\left(1+\frac{0.06}{4}\right)^{4\cdot 17} \implies 2250=P(1.015)^{68} \\\\\\ \cfrac{2250}{(1.015)^{68}}=P\implies 817.51\approx P\)

The amount for deposited into account is, $817.5.

We have to given that,

Interest rate = 6%

Final amount = $2250

Time = 17 years

Now, We can use the formula,

\(A = P (1 + \frac{r}{n} )^{n*t}\)

Where, A = Final amount

P = Principal amount

r = Interest rate

n = 4

t = time in years

Here, A = 2250,

r = 6% = 0.06

t = 17 years

Substitute all the values, we get;

\(2250 = P(1 + \frac{0.06}{4} )^{4*17}\)

2250 = P(1 + 0.015)⁶⁸

2250 = P (1.015)⁶⁸

P = 817.5

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Answer:

61,845,823

Step-by-step explanation:

had my trusty paper and pen next to me my guy aka a calculator

Answer:

10.15

Step-by-step explanation:

47.5-37.35=10.15

The range for the y = 2x+4 is (-∞,∞) .

The Range for a function y=f(x) is defined as set of all possible values of the dependent variable after substituting the value from domain .

For Example : the range for function y=x² is [0,∞) as x² will give only non negative values .

In the question ,

the given function is y=2x+4 ,

On comparing this with the equation of line y=mx+c

we get , slope(m)= 2 and the y intercept(c) = 4 ,

hence this function represents the straight line

So, the range of the function is (-∞,∞) .

Therefore , the range for the y = 2x+4 is (-∞,∞) .

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since all sides are equal, which means all angles must also be equal to one another

all angles =60°

solving 7x-3=60

7x=63

x=9

similarly 11 y+5=60

11y=55

y=5

a) we obtain the difference equation: 5Pn-1 * (1 - Pn) + (1/6) * (1 - Pn-1)., b) Pn = (6/11)^n + (1/11) * [(6/11)^(n-1) + (6/11)^(n-2) + ... + 1].

The given problem involves finding the probability, denoted by Pn, of throwing an even number of sixes when throwing a fair die n times. To solve this problem, we can derive a difference equation relating Pn to its previous terms, and then solve the equation to obtain an explicit formula for Pn.

a) To derive the difference equation, we consider the two possible cases for the last throw. If the last throw results in a six, then the number of sixes in the first (n-1) throws must be odd, so Pn = (1/6) * (1 - Pn-1). If the last throw does not result in a six, then the number of sixes in the first (n-1) throws must be even, so Pn = (5/6) * Pn-1. Combining these two cases, we obtain the difference equation: 5Pn-1 * (1 - Pn) + (1/6) * (1 - Pn-1).

(b) To solve the difference equation, we assume that P0 = 1 (since there are zero throws, the probability of getting an even number of sixes is 1). Using this assumption, we can recursively compute Pn using the difference equation. After simplifying the equation, we find that Pn = (6/11) * Pn-1 + (1/11). By continuing this recursion, we can find an explicit formula for Pn, which is Pn = (6/11)^n + (1/11) * [(6/11)^(n-1) + (6/11)^(n-2) + ... + 1].

Note: The given solution assumes the initial condition P0 = 1. If a different initial condition is provided, it may lead to a different explicit formula for Pn.

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Answer:

R U A girl?

Step-by-step explanation:

The quadratic equation which satisfy all the condition is y= -(x+4) (x- 10)

What is the simple quadratic formula?

The quadratic formula is as follows. The equation Ax2+Bx+C=0 can be divided by A to get x2+B/Ax+C/A=0, and the procedure repeated to get the more generic version.

How do you square a number?

How to use the Quadratic Formula to solve a quadratic equation.

Ax2 + bx + c = 0 is the quadratic equation in standard form. Find the values of a, b, and c.

the quadratic formula in writing. Then enter the values for a, b, and c.

Simplify.

Verify the answers.

Given that :

Roots are (-4, 0) and (10, 0)

and goes through  the point (5,45)

So as we can see that that only second and third option satisfy the roots and the third one satisfy the point conditions.

hence the quadratic equation which satisfy all the condition is y= -(x+4) (x- 10)

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The exact expression for the electrostatic potential at a point P in the x, y plane at a distance r from the center of the quadrupole is given by V(r) = k [Q/(r2 + D2)1/2 – Q/[(r2 + 2d + D2)1/2]] + k [-2Q/D].

Let's consider that three charges are placed in a straight line along the z-axis, and the charges are +Q on z=+D, -Q on z=-D, and -2Q at z=0.

To find the electrostatic potential at a point P in the x, y plane at a distance r from the center of the quadrupole, let's proceed with the following steps:

To find the electrostatic potential at a point P in the x-axis, we need to consider that the distance from the charges that are on the axis is r, and the distance from the charges that are on the axis and are at +D and -D is d.

The distance from the charges on the axis and at 0 is x. Now we can write,

V(x) = k [Q/(x2 + D2)1/2 – Q/[(x + d)2 + D2]1/2] + k [-2Q/D].

Now, we can substitute the values in the above expression and obtain,

V(x) = k [Q/(x2 + D2)1/2 – Q/[(x + d)2 + D2]1/2] + k [-2Q/D] .

Now, we need to use symmetry to argue that we can switch from x to r, which is given by r2 = x2 + y2.

Thus, the exact expression for the electrostatic potential at a point P in the x, y plane at a distance r from the center of the quadrupole is given by V(r) = k [Q/(r2 + D2)1/2 – Q/[(r2 + 2d + D2)1/2]] + k [-2Q/D].

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The vertical component of velocity can be zero at specific points in the motion of an object.

What is Velocity?

Velocity is a vector quantity that describes the rate of change of an object's position in space over time. It is defined as the displacement of an object divided by the time interval during which the displacement occurred.

The vertical component of velocity can be zero at specific points in the motion of an object. This occurs when the object reaches the highest point in its vertical motion and begins to fall back down. At this point, the vertical component of velocity changes direction from upward to downward, and its magnitude becomes zero. This moment is known as the "instant of maximum height" or "instant of maximum altitude." Beyond this point, the vertical component of velocity becomes negative, indicating that the object is moving downward.

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The appropriate alternative hypothesis is "The mean of a population is greater than 125".

An alternative hypothesis is a statement that is formulated to compete with a null hypothesis, and it generally contradicts or negates the null hypothesis.Therefore, the appropriate alternative hypothesis out of the given options would be "The mean of a population is greater than 125".Option A states that the mean of a population is equal to 125, which is similar to the null hypothesis, so it cannot be an alternative hypothesis.Option B states that the mean of a sample is equal to 125, which cannot be considered an appropriate alternative hypothesis as it is about a sample, not a population.The last option C is also incomplete, and thus, it cannot be considered as an alternative hypothesis.

An alternative hypothesis is a statement that is formulated to compete with a null hypothesis, and it generally contradicts or negates the null hypothesis.Therefore, the appropriate alternative hypothesis out of the given options would be "The mean of a population is greater than 125".Option A states that the mean of a population is equal to 125, which is similar to the null hypothesis, so it cannot be an alternative hypothesis.Option B states that the mean of a sample is equal to 125, which cannot be considered an appropriate alternative hypothesis as it is about a sample, not a population.The last option C is also incomplete, and thus, it cannot be considered as an alternative hypothesis.

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Answer:

37

Step-by-step explanation:

Add all the numbers up and you will get 370. How many numbers are there in total? 10 right so you divide 370 with 10 and get 37.

hope this help

Answer:

I'm uploading a picture. Hope this helps.

Step-by-step explanation:

Step-by-step explanation:

Given the function, f(x) = -3x + 4, you basically need to choose any input (x-value) and substitute those values into the function.

       f(0) = -3(0) + 4

       f(0) = 0 + 4

       f(0) =  4 [this is the value of your final column, in the f(x)].

   2. f( 1 ) = -3( 1 ) + 4, where the input is x = 1.

       f( 1 ) = -3( 1 ) + 4

       f( 1 ) = -3 + 4

       f( 1 ) =  1 [this is the value of your final column, in the f(x)].

   3. f(2) = -3(2) + 4, where the input is x = 2.

       f(2) = -6 + 4

       f(2) = -2 [this is the value of your final column, in the f(x)].

All you need to do is plot the following points on your graph:

{(0, 4), (1, 1), (2, -2)}  

Answer:

The answer is

Step-by-step explanation:

Circumference of a circle is πd

Where d is the diameter

From the question

d = 40 feet

Circumference of the circle is

40π

= 125.66

= 126 feet to the nearest whole number

Hope this helps you

Answer:

it’s probably option 1 and the other person explained so yeah

if the level of significance of a hypothesis test is raised from .01 to .05, then  the probability of a Type II error will decrease when the level of significance of a hypothesis test is raised from .01 to .05. (option a)

This change in the level of significance does not directly affect the probability of a Type II error. A Type II error occurs when we fail to reject the null hypothesis, even though it is false. This means that we have concluded that there is no relationship between the variables, even though there actually is one.

The probability of a Type II error depends on several factors, such as the sample size, the effect size, and the level of significance. In general, as the level of significance increases, the probability of a Type II error decreases.

This is because when we are more lenient in rejecting the null hypothesis, we are more likely to detect any real relationship that exists between the variables.

Therefore, the correct answer to your question is (a)

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The hypergeometric probability function is based on the counting rule for combinations.

This rule states that if you have two sets of items, with one set containing n1 items and the other containing n2 items, the number of possible combination of r items that can be taken from the two sets is equal to n1+n2 choose n1. This means that you have to select n1 items from the first set, then n2 items from the second set. This function is used in probability calculations to determine the probability of selecting a certain number of items from one set, given a certain number of items from the other set. It is also used to calculate the probability of a certain event occurring when items are randomly selected from two sets.

The hypergeometric probability function can be used to calculate the probability of drawing a certain number of items from a given set. It can also be used to calculate the probability of a certain event occurring. For example, if you are playing a game where you draw 5 balls out of a bag of 20, you can use the hypergeometric probability function to calculate the probability of drawing a certain number of balls from the bag.

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The value of the expression Z² + Q² is 4321

The radius of the chocolate spheres is given as:

r = 2

The maximum number of chocolates that can fit in a spherical capsule is calculated as:

Max = R³/r³

Where:

R represents the radius of the sphere.

For the spherical capsule whose radius is 8 inches, we have:

Z = 8³/2³

Evaluate

Z = 64

For the spherical capsule whose radius is 5 inches, we have:

Q = 5³/2³

Evaluate

Q = 15.625

Remove decimal

Q = 15

So, we have:

Z² + Q² = 64² + 15²

Evaluate the exponent

Z² + Q² = 4096 + 225

Evaluate the sum

Z² + Q² = 4321

Hence, the value of Z² + Q² is 4321

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Notice that AD also creates two supplementary angles, BDA and ADE. Let y be the measure of the smaller angle, ADE; then the measure of the larger angle, BDA, is 180° - y.

Since AD bisects angle A, we have by the law of sines

sin(A/2)/x = sin(y)/8

and

sin(A/2)/6 = sin(180° - y)/12

Now,

sin(180° - y) = sin(180°) cos(y) - cos(180°) sin(y) = sin(y)

so that

sin(A/2) = x/8 sin(y)

and

sin(A/2) = 6/12 sin(y) = 1/2 sin(y)

Solve for x :

x/8 sin(y) = 1/2 sin(y)

x/8 = 1/2

x = 8/2

x = 4

Answer:

-3x+12 = -3(x-4)

-2(x+9) = −2x−18

Step-by-step explanation:

Answer:

4 and -9

Step-by-step explanation:

-3x+12=0

subtract 12 from both sides

-3x=-12

divide both sides by -3

x=4

-2(x+9)

distribute the -2 throughout

-2x-18=0

add 18 to both sides

-2x=18

divide both sides by -2

x= -9

Answer:

statement not complete

The simplification of rational expression (x²+6x-7)/(x²+9x+14) gives

(x-1)/(x+2). 

A polynomial or integer is simply resolved into components that, when multiplied together, produce the original or starting polynomial or integer.

The given expression is -

= (x²+6x-7)/(x²+9x+14)

Factorising both numerator and denominator;

= {x+7x-x-7} / {x+7x+2x+14}

= {x(x+7)-(x+7)} / {x(x+7)+2(x+7)}

= {(x+7)(x-1)} / {(x+7)(x+2)}

Cancel the (x+7),

= (x-1)/(x+2)

Therefore, the simplification of the given equation is (x-1)/(x+2).

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Answer:

56 m

Step-by-step explanation:

Area of Triangle - B x H/2

B = 16 m

H = 7 m

_________

Substitute the numbers with variables

Then solve

16 x 7/2

= 112/2

= 56 m

Answer:

5/4 and -5/4

Step-by-step explanation:

Solve means change b(x) to 0, factor and use zero product property (write two smaller equations)

This equation is a "difference of two squares" or "difference of perfect squares"

b(x) = 16x^2 - 25

0 = (4x - 5)(4x + 5)

Make two smaller equations.



4x-5=0 and 4x+5=0

Solve both of these separately.

4x - 5 = 0

add 5

4x = 5

divide by 4

x = 5/4 and,



4x + 5 = 0

subtract 5

4x = -5

divide by 4

x = -5/4

"zeros" are solutions are roots, are x-intercepts. These are all pretty commonly interchangeable. (Not exactly, technically for a mathematician) But for a student knowing what to do with a question, for all these:

find zeros

find solutions

find roots

find x-intercepts

Set it equal to 0 and solve.

The zeros are 5/4 and -5/4

Answer:

b(x)= (4x)^2-(5)^2

b(x)=(4x-5)(4x+5)

The zeros of b are 5/4 and -5/4