[tex] \: \: \: \: \: \: \: \: \: \: \: n\\ evaluate \: \: \: \: \: Σ \: (nCi)\\ \: \: \: \: \: \: \: \: \: \: \: \: i = 0[/tex]
Evaluate the summation​

Answer:

I believe it should be d

Step-by-step explanation:

The value of the function g(x) = x -3/2x + 1 for x = -1 is g(-1) = 4

The function is given as:

g(x) = x -3/2x + 1

The value is given as:

x = -1

Substitute the known values in the above equation

i.e. we substitute the -1 for x in the above equation

So, we have:

g(-1) = -1 -3/2(-1) + 1

Expand the bracket

g(-1) = -1 -3/-2 + 1

Evaluate the sum and the difference

g(-1) = -4/-1

Evaluate the quotient

g(-1) = 4

Hence, the value of the function g(x) = x -3/2x + 1 for x = -1 is g(-1) = 4

So, the complete parameters are:

g(x) = x -3/2x + 1

x = -1

g(-1) = 4

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The amount add to the borrower's monthly payment is $313.33.

Given that lender requires PMI that is 0.8% of the loan amount of $470,000.

A loan's PMI, or personal mortgage insurance, is a type of mortgage insurance used by lenders when making traditional loans such as home loans. A PMI helps cover the loss to the lender (bank) if the borrower stops making monthly mortgage payments on their home loan. Therefore, the PMI can be described as a kind of risk mitigation tool for the bank when the borrower defaults on their EMIs (monthly mortgage payments). So, PMI for a borrower is an additional cost or payment for the borrower on top of his monthly payments i.e. EMI.

Thus, the additional amount of dollars that the borrower has to pay for the PMI on his loan along with his monthly mortgage payments

= Principal Loan amount × (PMI/12)

= $470,000 × (0.8%/12)

= $470,000 × (0.008/12)

= $470,000 × 0.0006666667

=$313.333349

Hence, the additional monthly payment for PMI where lender requires PMI that is 0.8% of the loan amount of $470,000 is $313.33.

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a. Given the 2nd order ODE

[tex]y''(x) = 4y(x) + 4[/tex]

if we substitute [tex]z(x)=y'(x)+2y(x)[/tex] and its derivative, [tex]z'(x)=y''(x)+2y'(x)[/tex], we can eliminate [tex]y(x)[/tex] and [tex]y''(x)[/tex] to end up with the ODE

[tex]z'(x) - 2y'(x) = 4\left(\dfrac{z(x)-y'(x)}2\right) + 4[/tex]

[tex]z'(x) - 2y'(x) = 2z(x) - 2y'(x) + 4[/tex]

[tex]\boxed{z'(x) = 2z(x) + 4}[/tex]

and since [tex]y(0)=y'(0)=1[/tex], it follows that [tex]z(0)=y'(0)+2y(0)=3[/tex].

b. I'll solve with an integrating factor.

[tex]z'(x) = 2z(x) + 4[/tex]

[tex]z'(x) - 2z(x) = 4[/tex]

[tex]e^{-2x} z'(x) - 2 e^{-2x} z(x) = 4e^{-2x}[/tex]

[tex]\left(e^{-2x} z(x)\right)' = 4e^{-2x}[/tex]

[tex]e^{-2x} z(x) = -2e^{-2x} + C[/tex]

[tex]z(x) = -2 + Ce^{2x}[/tex]

Since [tex]z(0)=3[/tex], we find

[tex]3 = -2 + Ce^0 \implies C=5[/tex]

so the particular solution for [tex]z(x)[/tex] is

[tex]\boxed{z(x) = 5e^{-2x} - 2}[/tex]

c. Knowing [tex]z(x)[/tex], we recover a 1st order ODE for [tex]y(x)[/tex],

[tex]z(x) = y'(x) + 2y(x) \implies y'(x) + 2y(x) = 5e^{-2x} - 2[/tex]

Using an integrating factor again, we have

[tex]e^{2x} y'(x) + 2e^{2x} y(x) = 5 - 2e^{2x}[/tex]

[tex]\left(e^{2x} y(x)\right)' = 5 - 2e^{2x}[/tex]

[tex]e^{2x} y(x) = 5x - e^{2x} + C[/tex]

[tex]y(x) = 5xe^{-2x} - 1 + Ce^{-2x}[/tex]

Since [tex]y(0)=1[/tex], we find

[tex]1 = 0 - 1 + Ce^0 \implies C=2[/tex]

so that

[tex]\boxed{y(x) = (5x+2)e^{-2x} - 1}[/tex]

6.a) The differential equation for z(x) is z'(x) = 2z(x) + 4, z(0) = 3.

6.b) The value of z(x) is [tex]z(x) = 5e^{2x} - 2[/tex].

6.c) The value of y(x) is [tex]y(x) = \frac{5e^{2x}}{4} - \frac{1}{4e^{2x}} -1[/tex].

The given ordinary differential equation is y''(x) = 4y(x) + 4, y(0) = y'(0) = 1 ... (d).

We are also given a substitution function, z(x) = y'(x) + 2y(x) ... (z).

Putting x = 0, we get:

z(0) = y'(0) + 2y(0),

or, z(0) = 1 + 2*1 = 3.

Rearranging (z), we can write it as:

z(x) = y'(x) + 2y(x),

or, y'(x) = z(x) - 2y(x) ... (i).

Differentiating (z) with respect to x, we get:

z'(x) = y''(x) + 2y'(x),

or, y''(x) = z'(x) - 2y'(x) ... (ii).

Substituting the value of y''(x) from (ii) in (d) we get:

y''(x) = 4y(x) + 4,

or, z'(x) - 2y'(x) = 4y(x) + 4.

Substituting the value of y'(x) from (i) we get:

z'(x) - 2y'(x) = 4y(x) + 4,

or, z'(x) - 2(z(x) - 2y(x)) = 4y(x) + 4,

or, z'(x) - 2z(x) + 4y(x) = 4y(x) + 4,

or, z'(x) = 2z(x) + 4y(x) - 4y(x) + 4,

or, z'(x) = 2z(x) + 4.

The initial value of z(0) was calculated to be 3.

6.a) The differential equation for z(x) is z'(x) = 2z(x) + 4, z(0) = 3.

Transforming z(x) = dz/dx, and z = z(x), we get:

dz/dx = 2z + 4,

or, dz/(2z + 4) = dx.

Integrating both sides, we get:

∫dz/(2z + 4) = ∫dx,

or, {ln (z + 2)}/2 = x + C,

or, [tex]\sqrt{z+2} = e^{x + C}[/tex],

or, [tex]z =Ce^{2x}-2[/tex] ... (iii).

Substituting z = 3, and x = 0,  we get:

[tex]3 = Ce^{2*0} - 2\\\Rightarrow C - 2 = 3\\\Rightarrow C = 5.[/tex]

Substituting C = 5, in (iii), we get:

[tex]z = 5e^{2x} - 2[/tex].

6.b) The value of z(x) is [tex]z(x) = 5e^{2x} - 2[/tex].

Substituting the value of z(x) in (z), we get:

z(x) = y'(x) + 2y(x),

or, 5e²ˣ - 2 = y'(x) + 2y(x),

which gives us:

[tex]y(x) = \frac{5e^{2x}}{4} - \frac{1}{4e^{2x}} -1[/tex] for the initial condition y(x) = 0.

6.c) The value of y(x) is [tex]y(x) = \frac{5e^{2x}}{4} - \frac{1}{4e^{2x}} -1[/tex].

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We conclude that 375 portions can be sold.

We know that 500 portions have been ordered, but only 5/6 of that was delivered, so the number of delivered portions is:

p = (5/6)*500 = 416.6

Which we can round to the next whole number, 417.

Now we know that 10% of these are given to the players and staff, then the number of portions that can be sold is the 90% of 417, which is:

N = 417*(90%/100%) = 417*0.9 = 375

We conclude that 375 portions can be sold.

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Step-by-step explanation:

A quadratic equation is a  equation with a degree of 2. Below are the 5 ways to solve a quadratic equation.

The graph of an exponential function shows a geometric increase or decrease using a curve

Exponential functions are inverse of logarithmic functions. The standard exponential function is expressed as:

y = ab^x

where

a is the base

x is the exponent

The graph of an exponential function shows a geometric increase or decrease using a curve. According to the function given there will a decrease rate due to the value of the rate value given which is less than 1. The graph of the function given is attached below;

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We conclude that the starting average grade is 79.17%

There are 50 students, let's say that the grades are measured between 1% and 100%.

And the average grade of the 50 students is A.

We know that after it increased by 20%, the average of the grades is 95.

Then we just need to solve the percentage equation:

95 = A*(1 + 20%/100%) = A*(1.2)

95/1.2 = A = 79.17

We conclude that the starting average grade is 79.17%

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Answer:

75%

Step-by-step explanation:

You need to do the following equation: x+20≤95 and you will have the answer. (I am sorry if it is wrong but this is what my teacher told the answer was. I put this answer and got it correct.) Hope it helped. Have a nice day.

The image of X after the dilation is (a) (4, 0)

From the figure, the coordinates of X are given as:

X = (4, 0)

The dilation is given as:

Do,1

This means that we dilate X across the origin by a scale factor of 1.

So, we have:

X' = 1 * (4 - 0, 0 - 0)

Evaluate

X' = (4, 0)

Hence, the image of X after the dilation is (a) (4, 0)

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Answer:

Step-by-step explanation:

2x + 5y = 8

      -5    -5

2x = 8 - 5y

divide both sides by 2

[tex]\frac{2x}{2} = \frac{8-5y}{2}[/tex]

divide by 2 undoes the multiplication by 2

x = [tex]\frac{8- 5y}{2}[/tex]

divide 8 - 5y by 2

x = - [tex]\frac{5}{2}[/tex] y + 4

Answer:

C

Step-by-step explanation:

the answer is c

The time requires to catch up to him will be 3 hours.

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance. Speed is a scalar quantity it does not require any direction only needs magnitude to represent.

Given that Hunter leaves his house to go on a bike ride. He starts at a speed of 15 km/hr. Hunter's brother decides to join Hunter and leaves the house 30 minutes after him at a speed of 18 km/hr.

The time will be calculated as below:-

30 minutes = 0.5 hour

15x = 18(x - 0.5)

15x = 18x - 9

-3x = -9

x = 3 hours

Therefore, the time requires to catch up to him will be 3 hours.

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1) Given - This is given in the question.

2) Reflexive Property of Equality - Anything is equal to itself

3) Substitution Property of Equality - Due to the given, substituting 118° for m∠1 and 62° for m∠2 will not change the equality of the equation

4) Simplify - No need to explain as they have already given this

5) Definition of Supplementary Angles - Two angles are supplementary only when the sum of their measures is 180°.

6) Converse of Same-side Interior Angles Theorem - If there is a transversal intersecting two lines and the same-side interior angles formed are supplementary, then the lines are parallel.

1) Given - It is given in the question

2) Vertical Angles Theorem - Vertical angles have the same measure, making their angles congruent

3) Transitive Property of Congruence - Since it's given that [tex]\angle1\cong\angle3[/tex] and in step 2 we showed that [tex]\angle3\cong\angle4[/tex], we can say that [tex]\angle1\cong\angle4[/tex]

4) Transitive Property of Congruence - Since we proved that [tex]\angle1\cong\angle4[/tex] and it's given that [tex]\angle4\cong\angle5[/tex], we can say that [tex]\angle1\cong\angle5[/tex]

5) Converse of Alternate Interior Angles Theorem - If a transversal intersects two lines and the measures of alternate interior angles formed are equal, then the lines are parallel.

Quadrilateral is a family of plane shapes that have four straight sides. Thus the sum of their internal angles is [tex]360^{o}[/tex]. Examples include rectangle, square, rhombus, trapezium, and kite.

A kite is a plane shape that has its adjacent sides to have equal measures.

The given diagram in the question is a kite that has its specific properties compared to other quadrilaterals.

Thus, the required proof is stated below:

Given: ΔCAV and ΔCEV

Prove that: ΔCAV ≅ ΔCEV

Then,

CE ≅ CA (length of side property of a kite)

EV ≅ AV (length of side property of a kite)

<ACV ≅ <ECV (bisected property of a given angle)

<AVC ≅ <EVC (bisected property of a given angle)

CV is a common side to ΔCAV and ΔCEV

Therefore it can be deduced that;

ΔCAV ≅ ΔCEV (Angle-Angle-Side congruent theorem)

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All values of x that satisfy 2x+2/x+7 >= 0 are represented as x >= -1

The inequality expression is given as:

2x+2/x+7 >= 0

Multiply both sides by x + y

2x+2 >= 0

Subtract 2 from both sides

2x > -2

Divide both sides by 2

x >= -1

Hence, all values of x that satisfy 2x+2/x+7 >= 0 are represented as x >= -1

See attachment for the number line of x >= -1

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Answer:

36Q

Step-by-step explanation:

multiply all together we have 36Q

Using the z-distribution, the margin of error for the 95% confidence interval used to estimate the population proportion is 0.0683 = 6.83%.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

For this problem, the parameters are given as follows:

[tex]n = 198, \pi = \frac{80}{198} = 0.404[/tex]

Hence the margin of error is:

[tex]M = 1.96\sqrt{\frac{0.404(0.596)}{198}} = 0.0683[/tex]

The margin of error for the 95% confidence interval used to estimate the population proportion is 0.0683 = 6.83%.

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The rational equation with the desired asymptotes and intercepts is given by:

[tex]f(x) = \frac{-10(x^2 - 3x - 18)}{9(x^2 - 5x + 4)}[/tex]

The vertical asymptotes are related to the roots of the  denominator, hence:

[tex]f(x) = \frac{a}{(x - 4)(x - 1)} = \frac{a}{x^2 - 5x + 4}[/tex]

The x-intercepts are related to the numerator of the function, hence:

[tex]f(x) = \frac{a(x + 3)(x - 6)}{x^2 - 5x + 4} = a\frac{x^2 - 3x - 18}{x^2 - 5x + 4}[/tex]

The y-intercept is to find a, hence, when x = 0, y = 5, thus:

-18a/4 = 5

18a = -20

a = -10/9

Hence the function is:

[tex]f(x) = \frac{-10(x^2 - 3x - 18)}{9(x^2 - 5x + 4)}[/tex]

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Answer:

<-3,3>

Step-by-step explanation:

Answer: A

Step-by-step explanation:

The total value of the prizes is [tex]1000+500+2(50)=1600[/tex].

The total cost of the tickets is [tex]1000(4.00)=4000[/tex].

So, the total loss is $2400.

Dividing this by 1000 tickets gives $-2.40.

Step-by-step explanation:

Monday has 6 different letters.

and we have therefore 6 positions to put letters.

so, for the first position we have 6 choices.

for the second position the 5 choices, and so on.

that makes all together

6! = 6×5×4×3×2×1 = 720

ways to arrange the letters.

if the arrangements must not begin with M, we are taking one choice away for the 1st position.

we can express that as all the ways with only 5 choices for the first position, or as the total number of possibilities minus the ones that start with M.

1.

5×5×4×3×2×1 = 600

2.

6! - 1×5! = 720 - 120 = 600

now, for the possibilities that start with M but do not end with Y.

that is the same as demanding that the second position does not have a Y.

so, the first position has only one choice, and the second position has one choice less :

1×4×4×3×2×1 = 96

Answer:

$2.00 each day so $2.00 x 5 = $10

The decision is to fail to reject the null given that p value is not ≤ 0.05.

The hypothesis

H0 = p = 0.63

H1 = p < 0.63

α = 0.05

sample proportion = 71/125 = 0.568

x = 71

n = 125

standard error of the proportion

√0.63(1-0.63)/125

= 0.0431

The null hypothesis follows a standard normal distribution. This is a left tailed test.

We are to reject the null if the p value is less than 0.05

p < 0.05

This probability test is a z probability test.

Z test = 0.568 - 0.63 / 0.0431

test statistic = -1.436

-Z0.05 =

Critical value =  -1.645

p(z < -1.436)

p value = 0.0755

The decision would be to fail to reject the null hypothesis. The reason would be due to the fact that p value is greater than significance.

P-value is not ≤ α 0.05

0.0755 > 0.05

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Answer:

0.00018

Step-by-step explanation:

formula:Divide the volume by 1e+6

The third side of the triangle falls between (50, 60).

Inequality triangle theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.

Therefore, the other two sides are 5 cm and 55 cm. The range of the third side x can be computed using inequality triangle theorem.

Hence,

x < 5 + 55

x < 60

And,

x > 55 - 5

x > 50

Therefore, 50 < x < 60.

Hence, the third side of the triangle falls between (50, 60).

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Answer:

x = 48/7

Step-by-step explanation:

There's two good ways to do this problem.

Option 1:

Translate "x varies directly as y" into the equation y=kx

Then you have to find k. After you "reset" your y=kx equation, fill in k and then solve for x. See image.

Option 2:

Translate "varies directly" into a proportion, which is two fractions equal to each other:

x/y = x/y

Fill in the three numbers given and cross multiply and solve to find the fourth number. See image.

Answer:

A cone has one -third times the volume of a cylinder with the same base and altitude. True

The answer is A. True.

Assuming the cylinder and cone have same base and altitude, the formulas are :

Based on this, we can understand that :

A cone has one-third times the volume of a cylinder with the same base and altitude.