What is the vertex of the graph of g(x) = (x + 1)2

Answer:the answer is 319.857 and round to 320

Step-by-step explanation:

To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.

To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.

First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.

Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.

Using the formula for the present value of an ordinary annuity, we have:

PV = P * (1 - (1+r)\(^{(-n)})\)/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.

Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)\({(-360)}\))/r.

Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.

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9514 1404 393

Answer:

  (a)  4 in²

Step-by-step explanation:

The volume of a rectangular prism is given by the formula ...

  V = Bh

where B is the area of the base, and h is the height of the prism.

We can find the area of the base by solving for B.

  B = V/h

  B = (12 in³)/(3 in)

  B = 4 in² . . . . . . . . . . matches the first choice

Answer:

The first table is correct

Step-by-step explanation:

x=Yellow   Prob

0               .5625

1                .375

2               .0625

The attached document shows a tree diagram with all 16 outcomes.  Each outcome has probability 1/16.

The numbers at the right show the numbe of yellows for each outcome.  There are 9 outcomes with 0 yellow (prob = 9/16).

There are 6 outcomes with 1 yellow (prob = 6/16)

There is 1 outcome with 2 yellow (prob = 1/16)

Sorry about the watermarks--distracting!

Based on the given set of values, we can note that the first table is correct

This refers to the calculations of the way an event is most likely to occur.

Hence, the table for  x=Yellow   Prob

0               .5625

1                .375

2               .0625

For each outcome, there is probability 1/16.

The numbers at the right show the number of yellows for each outcome. There are 9 outcomes with 0 yellow (prob = 9/16).

There are 6 outcomes with 1 yellow (prob = 6/16)

There is 1 outcome with 2 yellow (prob = 1/16)

Hence, because the calculated values are consistent with the values in the first table, then we can conclude that the first table is correct.

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Answer:

none.

Step-by-step explanation:

because FTP=ATJ,

P=A

J=F

The two triangles are not congruent. The correct answer is option A.

If two triangles are congruent, this means they are the same shape and the same size. By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.

In the image two triangles, ETP and ATJ are given. Angle F and angle J are equal due to the opposite angle property. Similarly, angle P and angle A are also equal by alternate angle property. But all the angles are not congruent.

Hence, the triangle FTP and ATJ are not congruent with each other.

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Answer: 2/90 = 1/45

Step-by-step explanation:

Hello!

Okay, so first we need to add like terms... so first, add the terms with the same variables. That gives us:

9x + 7y + 4 + y

Now add 7y and y

That gives us:

9x + 8y + 4

This can't be added anymore... this is as far as we can go because they are no longer like terms.

Answer: 9x+8y+4

Step-by-step explanation:

4x+7y+4+5x+y

9x+7y+4+y

9x+8y+4

Answer:

Step-by-step explanation:

A. 40

B. 28

C. 44

D. 25

Answer:

B. 68pi

Step-by-step explanation:

to find the surface area of a right cone given radius and slant height:

let A = surface area

let r = radius

let l = slant height.

A=pi*r*l + pi* r^2

plug in the values

A=pi*52+pi*16= about 213.62

The surface area of the cone is 68π sq. units.

The surface area of a figure is the number of unit squares it takes to cover the entire surface without gaps or overlaps. If a three-dimensional figure has flat sides, the sides are called faces. The surface area is the total of the areas of the faces.

Given that, the slant height and the radius of a cone is 13 units and 4 units respectively,

We need to find the surface area of the cone,

SA = π×r×l + π×r²

SA = π(4×13+16)

SA = 68π

Hence, the surface area of the cone is 68π sq. units.

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This is due to the fact that angles 2, 3, and 5 are interior angles of the triangle, and the total of the inner angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

A triangle is a closed, two-dimensional geometric object composed of three line segments, known as sides, that intersect at three locations, known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all sides equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles less than 90 degrees), right (one angle equal to 90 degrees), or obtuse (all angles greater than 90 degrees). The area of a triangle can be computed using the formula A = (1/2)bh, where A is the area, b is the triangle's base, and h is the triangle's height.

Regarding the given diagram, the following claims are always true:

m∠3 + m∠4 + m∠5 = 180°

m∠5 + m∠6 = 180°\s= m∠2 (the measure of the external angle at angle 2). (the measure of the exterior angle at angle 2). And because angles 2 and 3 are likewise interior triangle angles, we get m2 + m3 = m6, which can be rearranged to yield m5 + m6 = m3 + m4 + m5 = 180°.

m∠2 + m∠3 + m∠5 = 180°

This is due to the fact that angles 2, 3, and 5 are interior angles of the triangle, and the total of the inner angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

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Answer:

89.4

Step-by-step explanation:

Okay well if  149=100% and there is a 40% we just have to find 60% and to do that we just multiply 149 by 0.60 to get 89.4

149*0.60=89.6

9514 1404 393

Answer:

  C ≈ 0.00106455765168

Step-by-step explanation:

This is the sum of 13 terms of the geometric series that has 10000C/1.05 as the first term and a common ratio of 1/1.05. The sum S is given by ...

  S = a1(1 -r^n)/(1 -r) . . . . a1 is the first term, r is the common ratio

Using the known values, we have ...

  100 = (10000C/1.05)(1 -1.05^-13)/(1 -1/1.05))

  0.01 = C(1 -1.05^-13)/0.05

  C = 0.0005/(1 -1.05^-13) ≈ 0.0005/0.469679

  C ≈ 0.00106455765168

Answer:

C ≈ 0.00106455765168

Step-by-step explanation:

100 = (10000C/1.05)(1 -1.05^-13)/(1 -1/1.05))

 0.01 = C(1 -1.05^-13)/0.05

 C = 0.0005/(1 -1.05^-13) ≈ 0.0005/0.469679

 C ≈ 0.00106455765168

The sales tax was $0.57, and the total amount that Morgan paid for the meal, including tax and tip, was $24.13.When calculating the sales tax, we first need to know the rate of the sales tax.

In this case, the rate is 3%. To calculate the amount of the sales tax, we multiply the rate (expressed as a decimal) by the pre-tax amount of the bill. In this case, 3% as a decimal is 0.03, and the pre-tax amount of the bill is $19.05, so:

Sales tax = 0.03 x $19.05 = $0.57

This means that the sales tax on the bill was $0.57.

To find the total amount of the bill, including tax, we add the pre-tax amount and the sales tax. In this case, the pre-tax amount was $19.05, and the sales tax was $0.57, so:

Total bill = $19.05 + $0.57 = $19.62

Now, we need to calculate the tip that Morgan left. Morgan tipped 23% on the amount after the sales tax was added. This means that we need to calculate 23% of the total bill, which includes the sales tax. To do this, we first need to know 23% as a decimal, which is 0.23. Then, we multiply this decimal by the total bill:

Tip = 0.23 x $19.62 = $4.51

So the tip that Morgan left was $4.51.

To find the total amount that Morgan paid for the meal, including tax and tip, we add the pre-tax amount, the sales tax, and the tip. In this case, the pre-tax amount was $19.05, the sales tax was $0.57, and the tip was $4.51, so:

Total amount paid = $19.05 + $0.57 + $4.51 = $24.13

Therefore, the sales tax was $0.57, and the total amount that Morgan paid for the meal, including tax and tip, was $24.13.

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Given:

what word represents when the line intersects with the y-axis?

The intersection between a line and the y-axis gives:

the point of the y-intercept

The solution is B, (x, y, z) = (-1, 0, 0).

Eliminate z from the last two equations:

(y + 2z) + 2 (x - y - z) = 0 + 2 (-1)

2x - y = -2

Eliminate y from this and the first equation:

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

x = -1

Solve for y :

2x - y = -2

2 (-1) - y = -2

y = 0

Solve for z :

x - y - z = -1

-1 - 0 - z = -1

z = 0

Answer: 12.57

Step-by-step explanation: I got u

After solving;

(a) P(40.5<Y<48.9) = 0.3721

(b) P(40.5<Y<48.9|X=68.6) = 0.6075

(c) P(40.5<Y<48.9∣X>=68) = 0.3925

(d) In b and c we use conditional probability in bi-variate case. In a it is uni-variate normal distribution.

Given that;

μ(x) = 60.6  

σ(x) = 11.2  

μ(y) = 46.8  

σ(y) = 8.4  

ρ = 0.94  

That is (X,Y) follows BVN(60.6,46.8,11.2,8.4,0.94)

(a) We have to find P(40.5<Y<48.9).

P(40.5<Y<48.9) = P[(40.5-μ(y))/σ(y) < (Y-μ)/σ(y) < (48.9-μ(y))/σ(y)]

Here Z = (Y-μ)/σ(y) follows N(0,1)

P(40.5<Y<48.9) = P{(40.5-46.8)/8.4 < Z < (48.9-46.8)/8.4}

P(40.5<Y<48.9) = P( -6.3/8.4 < Z < 2.1/8.4)

P(40.5<Y<48.9) = P(-0.75 < Z < 0.25)

P(40.5<Y<48.9) = p(0<Z<0.75)+p(0<Z<0.25)

P(40.5<Y<48.9) = 0.2734+0.0987

P(40.5<Y<48.9) = 0.3721

b) We have to find P(40.5<Y<48.9∣X=68.6).

We know that Y|X follows N(μ(y)+ρ σ(y)/σ(x) (x-μ(x)),σ^2(y)(1-ρ^2))

μ(y)+ρ σ(y)/σ(x) (x-μ(x)) = 46.8+0.94* 8.4/11.2 (X-60.6)

μ(y)+ρ σ(y)/σ(x) (x-μ(x)) = 46.8+0.705(X-60.6)

σ^2(y)(1-ρ^2) = 8.4^2(1-0.94^2)

σ^2(y)(1-ρ^2) = 70.56(1-0.8836)

σ^2(y)(1-ρ^2) = 70.56*0.1164  

σ^2(y)(1-ρ^2) = 8.2132

Y|X follows N(46.8+0.705(X-60.6),8.2132)  

X = 68.6

Y|X follows N(46.8+0.705(68.6-60.6),8.2132)  

N(46.8+5.64,8.2132)

N(52.44,8.2132)

P(40.5<Y<48.9|X=68.6)=p{(40.5-52.44)/√(8.2132)<Z<√(48.9-52.44)/√(8.2132)

P(40.5<Y<48.9|X=68.6) = P(-11.94/2.8658 < z < -3.54/2.8658)

P(40.5<Y<48.9|X=68.6) = p(-4.17 < z < -1.24)

P(40.5<Y<48.9|X=68.6) = 1-0.3925

P(40.5<Y<48.9|X=68.6) = 0.6075

c) Now we have to find the P(40.5<Y<48.9∣X>=68)

P(40.5<Y<48.9∣X>=68) = 1-0.6075

P(40.5<Y<48.9∣X>=68) = 0.3925

d) In b and c we use conditional probability in bi-variate case. In a it is uni-variate normal.

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The right question is given below:

Answer:

Y = -½x + 3/2

Y = -3x + 5

Y = 1/4x - 3¼

Step-by-step explanation:

Parallel implies they have the same gradient

Perpendicular implies the gradient is a negative reciprocal of the other.

The reflection of shape from x = -2 shown below.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

We have,

To reflect the figure from x= -2.

Then, the coordinates of object after reflection is

(-1, -1)

(1, -1)

(-1, -4)

(0, -4)

(1, -3)

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A repeating decimal is acceptable to use during calculations when you require a certain level of precision

A repeating decimal is acceptable to use during calculations when you require a certain level of precision, but it's important to keep in mind that the result will be an approximation rather than an exact value.

It is commonly used in situations where a rounded value is sufficient and the level of precision doesn't significantly impact the final result.

On the other hand, you should convert a repeating decimal to a fraction for calculations when you need an exact value or when further mathematical operations or comparisons are required.

Converting a repeating decimal to a fraction allows for precise calculations and eliminates any potential rounding errors associated with working with decimal approximations.

Converting a repeating decimal to a fraction involves identifying the repeating pattern and expressing it as a fraction. This allows for exact calculations and maintains the mathematical properties of fractions.

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Answer:

0.337 = 33.7% probability that one of the eight children has a food allergy.

Step-by-step explanation:

For each children, there are only two possible outcomes. Either they have a food allergy, or they do not. The probability of a child having food allergy is independent of any other child. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

7% of U.S. children 4 years of age or younger have a food allergy.

This means that \(p = 0.07\)

A day care program has capacity for 8 children in that age range.

This means that \(n = 8\)

What is the probability that one of the eight children has a food allergy?

This is P(X = 1).

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 1) = C_{8,1}.(0.07)^{1}.(0.93)^{7} = 0.337\)

0.337 = 33.7% probability that one of the eight children has a food allergy.

Answer:

-2,-4

Step-by-step explanation:

Answer:

100+100=200 it's an mathmatecial answer

Answer:

= 9

Step-by-step explanation:

1/2 (12) +3 = 9

Hope this helps!

The ratio of Student Ambassadors to total Students in Mr. Thompson's class is 1:4.

Ratios and proportions are two fundamental concepts in mathematics that are used to compare quantities and express relationships between them.

A ratio is a comparison of two quantities that are expressed in the same units. Ratios are typically written in the form of "a:b" or "a to b", where a and b are two quantities being compared. For example, the ratio of the number of boys to the number of girls in a class of 20 students might be 3:2, indicating that there are 3 boys for every 2 girls.

A proportion is a statement that two ratios are equal. Proportions are used to solve problems involving ratios by setting up an equation that equates two ratios.

The total number of students in Mr. Thompson's class is 6 + 18 = 24.

The ratio of Student Ambassadors to total Students is 6:24, which can be simplified by dividing both the numerator and denominator by 6 to get 1:4.

Therefore, the ratio of Student ambassadors to total Students in Mr. Thompson's class is 1:4.

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Answer:

400^2 = 160 000

Step-by-step explanation:

The square of a number means the product of a number by itself, while the perfect square ... For example, the number 9 is a perfect square because it can be expressed as a product of ... A square football pitch has a perimeter of 400 meters.