Given a positive integer n, assign true to is_prime if n has no factors other than 1 and itself. (remember, m is a factor of n if m divides n evenly.)

 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:

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°.

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 : 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]

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.

Answer with explanation:

Principal = $ 1000

Time = 2 years

Rate of Interest = 7 %

Since of rate of interest is compounded monthly,

then, [tex]R=\frac{7}{12}\\\\T=2 \times 12 =24[/tex]

Amount after 2 years

 [tex]=P\times [1 +\frac{R}{100}]^T\\\\=1000 \times [1+\frac{7}{1200}]^{24}\\\\=1000 \times [\frac{1207}{1200}]^{24}\\\\=1000 \times (1.00583)^{24}\\\\=1000\times 1.14972\\\\=1149.72[/tex]

Amount after 2 years, when rate of interest, is compounded monthly=$ 1149.72  

To decrease the concentration of a 15% alcohol solution to 7%, 16 mL of water needs to be added to the original 14 mL solution.

The problem involves using the concept of concentration dilution that is C1V1 = C2V2, where C1 is the initial concentration, V1 is the initial volume, C2 is the final concentration, and V2 is the final volume.

First, we need to convert the percentage to decimal so, C1=0.15 (15% as a decimal) and C2=0.07 (7% as a decimal). We know V1=14 mL (the starting volume of the 15% alcohol solution) and we are solving for V2.

Insert the known values into the equation and solve for V2: (0.15)(14) = (0.07)(V2). After calculation, V2 is approximately 30 mL.

To figure out how much water should be added to reduce the concentration from 15% to 7%, subtract the initial volume from the final volume: 30 mL - 14 mL = 16 mL.

So 16 mL of water needs to be added to the 15% alcohol solution to reduce the concentration to 7%.

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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.

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.

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.

Answer:

189 is the answer

Step-by-step explanation:

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.