1. Fourteen cars were randomly chosen at a used car lot. The age of each car and its sale price are shown in
the following table.

(a) The common ratio R is 3/10.

What do you mean by Geometric progression?

Every following word in a sequence known as a geometric progression (GP) is created by multiplying every previous term by a constant amount, or "common ratio." Another name for this progression is a pattern-following geometric sequence of numbers.

To find out the common ratio we have to divide the second term by the first term,

in the given example to find out the common ratio we have to divide [tex]P_{2[/tex] by  [tex]P_{1}[/tex],

so, we are getting, common ratio(R)= 9/30

                                                          =  3/10

Hence,The common ratio(R) is 3/10.

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Answer:

[tex] \huge{ \boxed{y = 4x + 10}}[/tex]

Step-by-step explanation:

The equation of a line in slope-intercept form is given by

[tex] \bold{y = mx + c}[/tex]

where

m is the slope

c is the y intercept

From the question

m = 4

In order to find c we substitute the point (−3,−2) into the equation y = mx + c

We have

[tex] - 2 = 4( - 3) + c \\ - 2 = - 12 + c \\ c = - 2 + 12 \\ c = 10[/tex]

We now substitute m and c into the equation

We have the final answer as

[tex] \bold{y = 4x + 10}[/tex]

Hope this helps you

The fraction of a tank is used daily is 1/15.

Given that, Jordan uses 1/3 of a tank of gas each week on their commute for 5 days.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Average tank of gas used = Total tank of gas/Number of days

= 1/3 ÷ 5/1

= 1/3 × 1/5

= 1/15

Therefore, the fraction of a tank is used daily is 1/15.

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by converting the decimal number 0.65 to the simples fraction, the result will be 13 / 20

The given decimal number = 0.65

The decimal number consist of a whole number part and fractional part. The whole number and the fractional part are separated by a decimal point.

Multiply the given decimal number by 100/100

Then the result will be

0.65 × (100/100) = (0.65×100) / 100

Multiply the numerator terms

(0.65×100) / 100 = 65 / 100

Divide both numerator and denominator by 5

Then the expression will be

(65/5) / (100/5) = 13 / 20

Hence, by converting the decimal number 0.65 to the simples fraction, the result will be 13 / 20

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Answer:

It can send 2,666 kids to school for a year.

Answer: Yellow Greed

Step-by-step explanation: Maths

Answer:

Step-by-step explanation:

The question about how many people ONLY had a drink is asking to solve some simultaneous equations .   Know this?

People = 92

soup = SP = 33

sandwich = SW = 45

drink = D = 52

9(SP+SW+D)

5(SP+SW)

10(SW+D)

5(SP+D)

for a drink 9+10+5 people had a drink with something else

24 had a drink with something else so 52-24=28 only had a drink

28 people only had a drink

The derivative of the given function is 4x³ / (x²+1) ²

What is derivative mean?

d(u/v) = [ u(dv/dx) + v(du/dx) ] / v²

Given:

f(x) = x²/x²+1

Applying the formulae:

=  x²[ d(x²+1)/dx] + (x²+1) [ d(x²)/dx ] / (x²+1) ²

= x²(2x+0) + (x²+1)2x / (x²+1) ²

= 2x³ + 2x³ / (x²+1) ²

= 4x³ / (x²+1)²

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The length and width of the rectangle is 31 inches and 7 inches.

Given:

The length of a rectangle is 10 inches more than 3 times the width and the area is 217 square inches.

Let l and w be the length and breadth.

l = 10 + 3w

lw = 217

w = 217/l

l = 10 + 3(217/l)

l = 10 l + 651 / l

[tex]l^{2} -10l -651=0[/tex]

on solving

l = 31 inches

lw = 217

w = 217/31

w = 7 inches.

Therefore the length and width of the rectangle is 31 inches and 7 inches.

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Each  player will get 9 cards.

According to our question-

total people= 6

cards=52

52/6= 8.66

rounding off

=9

hence, each  player will get 9 cards.

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The result of adding the two given equations (-2x + 7y = -5 and -2x - 4y = 6) is -4x + 3y = 1

From the question, we are to determine the result of adding the two given equations.

The given equations are

-2x + 7y = -5 and -2x - 4y = 6

Now, we will add the equations

    -2x + 7y = -5

+ ( -2x - 4y = 6

------------------------------

-2x + (-2x) + 7y + (-4y) = -5 + 6

-2x - 2x + 7y - 4y = 1

Simplifying

-4x + 3y = 1

Hence, the result of adding the equations is -4x + 3y = 1

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The probability of the event E i.e an odd number less than 9 is 0.4.

The probability of an event is a ratio of number of favorable outcomes to total number of outcomes. The sum of all probabilities of events must be equal to one. The probability of an event must not be greater than 1.

In event E i.e an odd number less than 9, the number of favorable outcome is 4 i.e. {1,3,5,7}.

The total number of outcomes is whole set S i.e. 10.

So, the probability of event E will be,

P(E) [tex]=\frac{4}{10}[/tex]

=0.4

Therefore, the probability of the event E i.e an odd number less than 9 is 0.4.

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Answer:

$247,517

Step-by-step explanation:

Hello,

Assets

(Car Value) $29,850

(Savings Account Balance) $12,409

(Treasury Bonds) $10,000

(Checking Account Balance) $19,419

(Home Value) $194,450

29850+12409+10000+19419+194450 = 266128

Liabilities

(Car Loan) $10,560

(Student Loans) $13,824 since the students loans are payed of we don't include it into the final net worth.

(Credit Card Balance) $8,051

10560+8051=18611

assets - liabilities = net worth

266128 - 18611 = 247517

So, if the banker pays off the students loans of a credit union banker their net worth will be $247,517.

Answer: 20 tis it

Step-by-step explanation:

my man

Answer:

46/273

Step-by-step explanation:

To add fractions, they must have a common denominator. To set one, find a common multiple of both denominators. Simply multiply them together if it proves difficult.

7 x 39 = 253

Now set the denominators to this number and multiply the numerators by the opposite fraction's denominator.

39/259 + 7/253 = 46/253
This simplifies to 2/11

So, 1/3 + 1/39 = 2/11

Answer:

if you mean 0.14 + 3.5 the answer is 3.64

Step-by-step explanation:

Line the numbers and decimal point when adding

The number is defined by the two inequalities:

x > -3

x  ≤ -6

If we define x as the number, the number increased by 3 is written as:

x + 3

If this is greater than zero or less than or equal to negative three, we can write two inequalities:

x + 3 > 0

x + 3 ≤ -3

Solving both inequalities for x (isolting it) we will get:

x > 0 - 3

x > -3

and:

x  ≤ -3 - 3

x  ≤ -6

So we have the two inequalities that define the number:

x > -3

x  ≤ -6

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The growth formula for the given population is P = 182eⁿˣ and the population in 2004 is 186.98 million

Growth function:

Basically, the growth function means the pattern of data that shows greater increases with passing time, creating the curve of an exponential function.

Given,

A country's population in 1994 was 182 million. In 2002 it was 186 million.

Here we need to find the growth formula and the population in 2004.

According to the given problem, let us consider that the

final population P,

the starting population A, and

the time passed t.

Here we need to determine the value of the growth factor k.

And it can be calculated using the information for the years 1994 and 2002.

Here we know that, A will be 182 million (the population in 1994), P will be 186 million (the population in 2002), and t will be 8 years (the number of years between 1994 and 2002):

⇒186 = 182eⁿˣ⁸

⇒186/182 = e⁸ⁿ

Now, by applying ln to both sides of the equation:

⇒ln(186/182) = ln(e⁸ⁿ)

Using the laws of logarithms:

=> 8n = ln(186) - ln(182)

=> n = [ln(186) - ln(182)] / 8

=> n = 0.0027

Now, let's use this information to determine P in 2004.

Here the value of A will still be 182 million, but t will be 10 years.

Now, we have to apply these values then we get,

=> P = 182e⁰°⁰⁰²⁷ˣ¹⁰

=> P = 182e⁰°⁰²⁷

=> P = 182 x 1.0273

=> P = 186.98

Therefore, there are  186.98 million in 2004.

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The values of f(2) = 0 & f(3) = 2.

Here given that,

f(0) = f(1) = 1

f(n+1) = (n)/(n-1)

We have to solve the equation if n = 1:

putting the value of n = 1 in the given equation f(n+1) = (n)/(n-1)

= f(1+1) = 1/(1-1)

= f(2) = 0

In the same way we have to solve the equation if n = 2:

putting the value of n = 2 in the given equation f(n+1) = (n)/(n-1)

= f(2+1) = 2/(2-1)

= f(3) = 2/1

= f(3) = 2

Hence the answer is the values of f(2) = 0 & f(3) = 2.

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The required greatest common factor is given as 6zx¹⁰t.

Given that,
To determine the greatest common factor among the expressions,

The greatest common factor is defined as a group of the set of numbers that is the most considerable and greatest factor that all the numbers include of.

Here,
Given expression,
=  6zx⁶tx⁴, 30zx⁸tx³, 18zx⁵tx⁵
Taking common 6zx¹⁰t,
= 6zx¹⁰t{1 , 5x³, 3}

Thus, the required greatest common factor is given as 6zx¹⁰t.

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Answer:

3) m= 3/310

4) x > -1

6) 1:a)-4

2:b)-2

3:c)2

4:d)4

7) f(-4.2)=46.06

Step-by-step explanation:

hope this helps

Answer:

[tex]x=-\frac{43}{3}[/tex]

Step-by-step explanation:

[tex]-4(6x+7)=-316 \\ \\ 6x+7=-79 \\ \\ 6x=-86 \\ \\ x=-\frac{43}{3}[/tex]

Answer:

x=12

Step-by-step explanation:

hope this helps! -4(6x + 7) = -316=x=12

Answer:

5+-

[tex]5 + - x {}^{2} [/tex]

[tex] - x {}^{2} + 5[/tex]

Answer: 1/8, Division equation: 1/3 divided by 8/3

Step-by-step explanation:

Step 1: Write this problem as an equation, of means multiply so the equation is 1/3 x 3/8.

Step 2: Solve the equation by multiplying the numerators and the denominators. You get 3/24.

Step 3: Simplify by dividing the numerator and denominator by their gcf. In this case it is 3. So, 1/3 of 3/8 is 1/8.

Step 4: Now we need to get the division equation of 1/3 x 3/8, for this you do the same thing as if we had to actually solve the division equation with fraction, just for changing multiplication to division instead. I am talking about keep change flip. You keep the first fraction the same. you change the operation to it's opposite ,and you flip the numerator and denominator in the second fraction. When we do this we get our division equation of 1/3 divided by 8/3.

Answer: The ratio of the total number of marbles in Orlandria’s marble collection is 7:28, where 7 is the yellow marbles and 28 is the total number of marbles Orlandria has.

Examining the rainfall data for the two periods a conclusion is that the range of the values are period 1 has low variability while period 2 has high variability

period 1: 0.6

period 2: 4

The range in statistics refers to the distribution of data between the lowest and greatest value in the distribution. It is a widely used indicator of variation.

Measurements of variability provide you with descriptive statistics for summarizing your data set in addition to measures of central tendency.

By deducting the lowest value from the greatest value, the range is computed. A short range indicates low variability in a distribution, whereas a big range denotes significant variability.

The range is

period 1: 2.5 - 1.9 = 0.6

period 2: 4.7 - 0.7 = 4

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The viable solutions to the system will be (80, 90)

Gus is buying juice drinks, x, and snack packs, y, for a school picnic

The system of inequalities will be

x + y ≥ 150

1.5x + 3.5y ≤ 600

15x + 35y ≤ 6000

3x + 7y ≤ 1200.......equation 1

x + y ≥ 150....multiplied with 3

3x + 3y ≥  450...equation 2

3x + 7y - (3x + 3y) = 1200 - 450

3x + 7y - 3x - 3y = 750

4y = 750

y = 750/4

y ≤ 187.5

x + y ≥ 150.

x ≥ 150 - 187.5

x ≥ -37.5

Therefore, the viable solutions to the system will be (80, 90)

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a) Probability that the number of college students who say they use credit cards because of the rewards program is​ exactly​ two is;

P(X = 2) = 0.1419

b) Probability that the number of college students who say they use credit cards because of the rewards program is​ more than two is;

P(X > 2) = 0.9402

c) Probability that the number of college students who say they use credit cards because of the rewards program is​ between two and five inclusive is; P(2 ≤ X ≤ 5) = 0.8054

The formula for Binomial Probability distribution is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

where;

p is probability of success

n is number of trials

x = the number of expected successful outcomes

We are given;

p = 38% = 0.38

n = 10

Thus;

a) Probability that the number of college students who say they use credit cards because of the rewards program is​ exactly​ two is;

P(X = 2) = 10C2 * 0.38^(2) * (1 - 0.38)^(10 - 2)

P(X = 2) = 0.1419

b) Probability that the number of college students who say they use credit cards because of the rewards program is​ more than two is;

P(X > 2) = 1 - P(X ≤ 2)

P(X > 2) = 1 - [P(X = 0) + P(X = 1) + P(X = 2)]

P(X > 2) = 0.9402

c) Probability that the number of college students who say they use credit cards because of the rewards program is​ between two and five inclusive is;

P(2 ≤ X ≤ 5) =  [P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)]

P(2 ≤ X ≤ 5) = 0.8054

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If he  has allocated $67,050 for the cost of growing his crops. The number of acres of each crop that should  plant is Corn 270, Wheat 540, Soybeans 450.

Let c = corn

Let w = wheat

Let s = soybeans

C+W+S = 1260

45C + 60W + 50S = 67050

W =2C

Substitute equation 1 into equation 2

C + 2C +S = 1260

3C + S =1260

45C + 120C + 50S =67050

165C +50S =67050

Let eliminate S

165C+ 50(1260-3C) =67050

165C + 63000 - 150C= 67050

15C= 4050

Divide both side by 15c

c =4050/15

c = 270 (corn)

Wheat

W=2C

w = 2(270)

w= 540

S= 1260 - 3C

S= 1260- 3(270)

S =1260 -810

S = 450 (soybeans)

Therefore , 270, 540 and 450 are the acres that should be planted.

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