Six years from today you need $10,000. you plan to deposit $1,500 annually, with the first payment to be made a year from today, in an account that pays an 8% effective annual rate. your last deposit, which will occur at the end of year 6, will be for less than $1,500 if less is needed to reach $10,000. how large will your last payment be?

Answer : Option A

Explanation:

we can clearly see that from x+ y=5 we can substitute  y = 5-x in y = 9x^2

Option B is clearly incorrect  x can not be y -5

Option C  is incorrect because y can not be 5 +x

Option D is incorrect because  its y = 9x^2 not y^2 =9x^2 so y can not be 3x

if its y^2 = 9x^2 then  only  implies y =  3x

Answer:

Option 1st is correct

[tex]5-x= 9x^2[/tex]

[tex]y = 5-x[/tex]

Step-by-step explanation:

Given the equations:

[tex]y = 9x^2[/tex]      .....[1]

[tex]x+y = 5[/tex]         .....[2]

We can write equation [2] as:

[tex]y = 5-x[/tex]

Now, substitute this y value in [1] we have;

[tex]5-x= 9x^2[/tex]

Therefore, the system which is equivalent to the given system equation is,

[tex]5-x= 9x^2[/tex]

[tex]y = 5-x[/tex]

Answer:

189 is the answer

Step-by-step explanation:

The plane was traveling at 319 miles per hour heading east. This was determined by setting up equations for the distances covered in both directions, considering the speed difference, and solving for the eastward speed.

To find the speed at which the plane was traveling east, we need to set up two equations based on the given information.

Let's denote the speed of the plane heading east  [tex]v_e[/tex] and the speed of the plane heading south [tex]v_s[/tex]. According to the problem, [tex]v_s[/tex] = [tex]v_e[/tex] + 45 mph. We also know that the plane flew south for 4 hours and east for 6 hours, covering a total distance of 3,370 miles.

To represent the sum of distances covered in both directions, we use the equation:

4[tex]v_s[/tex] + 6[tex]v_e[/tex] = 3,370

Substituting [tex]v_s[/tex] with [tex]v_e[/tex] + 45 in the equation yields:

4([tex]v_e[/tex] + 45) + 6[tex]v_e[/tex] = 3,370

By simplifying and solving for [tex]v_e[/tex], we find the speed of the plane traveling east. Let's solve it step by step:

4[tex]v_e[/tex] + 180 + 6[tex]v_e[/tex] = 3,370

10[tex]v_e[/tex] + 180 = 3,370

10[tex]v_e[/tex] = 3,190

[tex]v_e[/tex] = 319 mph

Therefore, the plane was traveling at 319 miles per hour heading east.

total bill would be X=6.00 +0.08m

where m = minutes

X = total bill

so 11.52 = 6.00+0.08m

subtract 6 from each side

5.52 = 0.08m

 now divide both sides by 0.08

5.52/0.08 = 69

 he was billed for 69 minutes.

 To solve the following problems, we use the binomial probability equation:

P (r) = [n!/(n-r)! r!] p^r q^(n-r)

where,

n = total number of households = 8

r = number of sample

p = probability of success = 65% = 0.65

q = probability of failure = 0.35

A. r = 5

P (r=5) = [8! / 3! 5!] 0.65^5 0.35^3

P (r=5) = 0.28

B. r >5

P (r=6) = [8! / 2! 6!] 0.65^6 0.35^2

P (r=6) = 0.26

P (r=7) = [8! / 1! 7!] 0.65^7 0.35^1

P (r=7) = 0.14

P (r=8) = [8! / 0! 8!] 0.65^8 0.35^0

P (r=8) = 0.03

Therefore total is:

P (r>5) = 0.26 + 0.14 + 0.03 = 0.43

C. r ≤ 5

P (r ≤ 5) = 1 - P (r>5)

P (r ≤ 5) = 1 – 0.43

P (r ≤ 5) = 0.57

Answer:

Step-by-step explanation:

The act of reducing the selling price of products in order to attract costumers is called Price Reduction. This comprehends a marketing strategy.

Answer: b. [tex]x\geq 0[/tex] , where x is the positive real numbers.

Step-by-step explanation:

We Know that, The Set of all Possible values of independent variable is called Domain of the function.

Since, Exponential graph starting at point (0, 30000),

Thus, the initial value of value of independent variable is 0.

Also,  The given exponential function is approaching the x axis as it moves left to right.

Therefore, The Domain must contain the all positive real numbers.

Thus, the Domain of the given function is [tex]x\geq 0[/tex] , where x is the positive real numbers.

Therefore, Option b is correct.

Answer:

The correct option is A.

Step-by-step explanation:

The general form of an ellipse is

[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

Where, (0,0) is the center of ellipse, (±a,0) are x-intercepts and (0,±b) are y-intercepts.

From the given graph it is clear that the center of ellipse is (0,0), (±2,0) are x-intercepts and (0,±4) are y-intercepts. So, the equation of ellipse is

[tex]\frac{x^2}{(2)^2}+\frac{y^2}{(4)^2}=1[/tex]

[tex]\frac{x^2}{4}+\frac{y^2}{16}=1[/tex]

The shaded region is inside the ellipse, (0,0) lie in the solution set and the points lie on the ellipse are included in the solution set, therefore the sign of inequality is ≤.

[tex]\frac{(0)^2}{4}+\frac{(0)^2}{16}\leq 1[/tex]

[tex]0\leq 1[/tex]

This statement is true. The required inequality is

[tex]\frac{x^2}{4}+\frac{y^2}{16}\leq 1[/tex]

Therefore, the correct option is A.

Answer:

Step-by-step explanation:

By definition, a quadrilateral is a general term for a parallelogram and a rhombus. They are both 4-sided two-dimensional shapes with two sets of parallel sides. However, a rhombus is a special case. It has equal sides. Consequently, all its angles are equal. Therefore, the resultant drawing is alike to what's in the attached picture. But technically, all its sides are equal to 6 cm and all its angles are equal to 80°.

To calculate the salesperson's total annual pay, we add the commission earned from the total sales to the base salary. The commission is $12,500, and the base salary is $36,000, resulting in a total pay of $48,500.

The question asks us to determine the total pay for a salesperson with a base salary and a commission percentage on total sales. To find the salesperson's total pay for a year, we calculate the commission earned from total sales and add it to the base salary. The salesperson's commission is 2 1/2% of $500,000, which can also be written as 0.025. We calculate the commission by multiplying 0.025 by $500,000, which equals $12,500. Therefore, the total pay for the salesperson for that year is the sum of the base salary of $36,000 plus the commission of $12,500, which gives us $48,500.

To solve this problem, we make use of the z statistic. We are to look for the bottom 8% who has the shortest lifespan, this is equivalent to a proportion of P = 0.08. Using the standard distribution tables for z, the value of z corresponding to this P value is:

z = -1.4

Now given the z and standard deviation s and the mean u, we can calculate for the number of years of the shortest lifespan:

x = z s + u

x = -1.4 (0.7) + 2.4

x = -0.98 + 2.4

x = 1.42 years

Therefore the life span is less than about 1.42 years

The system of inequalities to determine the number of hamburger and hotdog buns Mr. Wu should purchase is x \\geq 2y for the quantity requirement, and 0.45x + 0.40y \\leq 60 for the budget constraint.

To determine how many hamburger buns (x) and hotdog buns (y) Mr. Wu can purchase for the concession stand, we need to set up a system of inequalities based on the given conditions. Since he needs at least twice as many hamburger buns as hotdog buns, we can express this requirement as an inequality: x \\geq 2y. Additionally, considering the cost of hamburger buns is $0.45 each and hotdog buns are $0.40 each, the total spending should not exceed $60. This gives us a budget constraint inequality: 0.45x + 0.40y \\leq 60. Therefore, the system of inequalities that can be used to determine the number of each kind of bun Mr. Wu should purchase is:

Answer:

advance booking is cheaper by 400 bahts or $10.

Step-by-step explanation:

Car rental cost in advanced booking = $35 per day

and

when the rented locally it is charged = 1800 bahts per day

it is given that,

$1 is equal to 40 bahts.

now,

Car rental cost in advanced booking =  35  × 40

                                                              = 1400 bahts

hence, when booking is done advance

  the cost is cheaper  by  1800 - 1400 = 400 bahts

hence, advance booking is cheaper by 400 bahts or $10.