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3 years ago

7

Store ABC sells 8 lbs. of oranges for $6.00. Store XYZ sells 14 lbs. or oranges for $11.20. Which store is less expensive, and b

y how much per pound? 1. ABC is less expensive by $.50 per pound 2. XYZ is less expensive by $.50 per pound 3. ABC is less expensive by $.05 per pound 4. XYZ is less expensive by $.05 per pound

1 answer:

mart [117]3 years ago

8 0

ABC-
8:6

XYZ-
14:11.20

ABC (unit rate)-
Divide both sides by 8...
1:0.75

XYZ (unit rate)-
Divide both sides by 14...
1:0.80

ABC is less, 0.80>0.75. The difference between the two is 0.05; 0.80-0.75=0.05.

So the answer is:
3. ABC is less expensive by $0.05 per pound.

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2. Which of the following are terms of the series with nth term T-3n +17? a) 80 b) 170 c)217 d) 312 e) 278 f) 3566

pishuonlain [190]

Answer:

The correct options are a,b,e and f.

Step-by-step explanation:

It is given that the nth terms of the series is defined as

$T_n=3n+17$

Subtract 17 from both the sides.

$T_n-17=3n$

Divide both sides by 3.

$\frac{T_n-17}{3}=n$

The term Tₙ is a term of given series if n is a positive integer.

(a) The given term is 80.

$n=\frac{80-17}{3}=21$

Since n is a positive integer, therefore 80 is a term of given series.

(b) The given term is 170.

$n=\frac{170-17}{3}=51$

Since n is a positive integer, therefore 170 is a term of given series.

(c) The given term is 217.

$n=\frac{217-17}{3}=66.67$

Since n is not a positive integer, therefore 217 is a term of given series.

(d) The given term is 312.

$n=\frac{312-17}{3}=98.33$

Since n is not a positive integer, therefore 312 is a term of given series.

(e) The given term is 278.

$n=\frac{278-17}{3}=87$

Since n is a positive integer, therefore 278 is a term of given series.

(f) The given term is 3566.

$n=\frac{3566-17}{3}=1183$

Since n is a positive integer, therefore 3566 is a term of given series.

Thus, the correct options are a, b, e and f.

7 0

3 years ago

Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probabilit

Verdich [7]

Answer:

a) Standard Deviation = 2.74

b) Significantly Low = values below 24.52 (or equal)

Significantly High = values above 35.48 (or equal)

Step-by-step explanation:

This is binomial probability distribution problem.

Where n = 40 [groups of 40, total trials]

p = 0.75 [probability of success]

a)

The formula for standard deviation is:

$Standard \ Deviation = \sqrt{np(1-p)}$

We know n = 40 and p = 0.75, so the standard deviation is:

$Standard \ Deviation = \sqrt{np(1-p)} \\Standard \ Deviation = \sqrt{(40)(0.75)(1-0.75)}\\ Standard \ Deviation = 2.74$

b)

the range rule of thumb tells us that usual range of values is within 2 standard deviation of the mean. First let's calculate mean.

We know,

Mean = n * p = 40 * 0.75 = 30

So

Mean - 2* Standard Deviation = 30 - 2(2.74) = 24.52

and

Mean + 2* Standard Deviation = 30 + 2(2.74) = 35.48

Significantly Low = values below 24.52 (or equal)

Significantly High = values above 35.48 (or equal)

8 0

3 years ago

Suppose an airplane climbs 15 feet up for every 40 feet it moves forward. What is the slope of this airplanes ascent?

Anastasy [175]

the rise over run is 15/40 so the slope of the airplanes ascent is 0.375 feet per foot is move forward

5 0

3 years ago

For integers a, b, and c, consider the linear Diophantine equation ax C by D c: Suppose integers x0 and y0 satisfy the equation;

Dmitrij [34]

Answer:

a.

$x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )$

b. x = -8 and y = 4

Step-by-step explanation:

This question is incomplete. I will type the complete question below before giving my solution.

For integers a, b, c, consider the linear Diophantine equation

$ax+by=c$

Suppose integers x0 and yo satisfy the equation; that is,

$ax_0+by_0 = c$

what other values

$x = x_0+h$ and $y=y_0+k$

also satisfy ax + by = c? Formulate a conjecture that answers this question.

Devise some numerical examples to ground your exploration. For example, 6(-3) + 15*2 = 12.

Can you find other integers x and y such that 6x + 15y = 12?

How many other pairs of integers x and y can you find ?

Can you find infinitely many other solutions?

From the Extended Euclidean Algorithm, given any integers a and b, integers s and t can be found such that

$as+bt=gcd(a,b)$

the numbers s and t are not unique, but you only need one pair. Once s and t are found, since we are assuming that gcd(a,b) divides c, there exists an integer k such that gcd(a,b)k = c.

Multiplying as + bt = gcd(a,b) through by k you get

$a(sk) + b(tk) = gcd(a,b)k = c$

So this gives one solution, with x = sk and y = tk.

Now assuming that ax1 + by1 = c is a solution, and ax + by = c is some other solution. Taking the difference between the two, we get

$a(x_1-x) + b(y_1-y)=0$

Therefore,

$a(x_1-x) = b(y-y_1)$

This means that a divides b(y−y1), and therefore a/gcd(a,b) divides y−y1. Hence,

$y = y_1+r(\frac{a}{gcd(a, b)})$ for some integer r. Substituting into the equation

$a(x_1-x)=rb(\frac{a}{gcd(a, b)} )\\gcd(a, b)*a(x_1-x)=rba$

or

$x = x_1-r(\frac{b}{gcd(a, b)} )$

Thus if ax1 + by1 = c is any solution, then all solutions are of the form

$x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )$

In order to find all integer solutions to 6x + 15y = 12

we first use the Euclidean algorithm to find gcd(15,6); the parenthetical equation is how we will use this equality after we complete the computation.

$15 = 6*2+3\\6=3*2+0$

Therefore gcd(6,15) = 3. Since 3|12, the equation has integral solutions.

We then find a way of representing 3 as a linear combination of 6 and 15, using the Euclidean algorithm computation and the equalities, we have,

$3 = 15-6*2$

Because 4 multiplies 3 to give 12, we multiply by 4

$12 = 15*4-6*8$

So one solution is

$x=-8$ & $y = 4$

All other solutions will have the form

$x=-8+\frac{15r}{3} = -8+5r\\y=4-\frac{6r}{3} =4-2r$

where $r$ ∈ Ζ

Hence by putting r values, we get many (x, y)

3 0

3 years ago

Bailey is sorting a set of 2 dimensional shapes as parallelograms or quadrilaterals. All but one of the shapes belong in both ca

likoan [24]

Answer:

The trapezoid

Step-by-step explanation:

All the other shapes have equal angels the trapezoid has only one pair of parallel side.

7 0

2 years ago