Solve the system of equations. \begin{aligned} &6x-5y = -32 \\\\ &-7x+8y=46 \end{aligned} ​ 6x−5y=−32 −7x+8y=46 ​ x=x=x, equals y=y=y, equals

Answer: c) 0.75

Step-by-step explanation:

Given : The probability of choosing a black marble is P(Black)= 0.36.

The probability of choosing a black and then a white marble is P( Black and white) = 0.27.

Then by conditional probability ,

The probability of the second marble being white if the first marble chosen is black = [tex]P(\text{white }|\text{Black})=\dfrac{\text{P( Black and white)}}{\text{P(Black}}[/tex]

[tex]=\dfrac{0.27}{0.36}=\dfrac{27}{36}=0.75[/tex]

Therefore , the probability of the second marble being white if the first marble chosen is black = 0.75

Final answer:

The probability of the second marble being white given that the first marble is black is calculated using conditional probability. By dividing the joint probability of choosing a black and then a white marble (0.27) by the probability of choosing a black marble (0.36), we find that the probability is 0.75.

Explanation:

The question asks to find the probability of the second marble being white given that the first marble chosen is black. The probability of choosing a black marble is given as 0.36, and the probability of choosing a black and then a white marble is 0.27. To find the probability of choosing a white marble after a black one, we use the concept of conditional probability, given by:

P(White | Black) = P(Black and White) / P(Black)

Here P(White | Black) is the probability of the second marble being white given that the first marble is black, P(Black and White) is the probability of choosing a black marble and then a white marble, and P(Black) is the probability of choosing a black marble. Substituting the given values:

P(White | Black) = 0.27 / 0.36 = 0.75

This means that the probability of the second marble being white, given that the first marble chosen is black, is 0.75, which corresponds to option (c) in the provided selections.

Answer:

Question 1

since triangles are similar

angle B = angle D

8x + 16 = 120

x = 13

Question 2

Ttiangles are similar

therefore, sides are in ratio

AB ÷ XY = BC ÷ YZ = AC ÷ XZ

substituting all values we get

BC = 22

BC = 22AC = 16

Answer:the truck load of fruit weigh 440 pounces

Step-by-step explanation:

Let the total weight of the truck load of fruit weigh x pounds.

The truck carries apples, grapes, and blackberries in the ratio of 4:3:4

The total ratio is the sum of the proportions of apples, grapes, and blackberries. It becomes 4+3+4 = 11

if the apples weigh 160 pounds, it means that

4/11 × x = 160

4x/11 = 160

4x = 160×11 = 1760

x = 1760/4

x = 440

Answer:

1 and 3

Step-by-step explanation:

For resolving an application problems using the two - order system, the following steps must be taken:

First assign two variables for the unknowns.

Second write two equations using the assigned variables.

Third solve the pair of equations.

Then, only 1 and 3 are steps in the process in solving application problems, using the two-order system

Answer:

The percent charge of Kanna's DS is 50%

Step-by-step explanation:

we know that

A Nintendo DS takes 4 hours to charge fully (100%)

4 hours is the same that 240 minutes

using proportion

Find out what percentage represent 108 minutes

[tex]\frac{100}{240}\ \frac{\%}{min} =\frac{x}{108}\ \frac{\%}{min}\\\\x=100(108)/240\\\\x=45\%[/tex]

Remember that

Kanna Kamui charge her DS from 5%

so

[tex]5\%+45\%=50\%[/tex]

therefore

The percent charge of Kanna's DS is 50%

To figure out the charge percentage of Kanna's DS, we need to know the time it takes for a full charge and the time Kanna's DS was charged. The calculation (108 minutes charged / 240 minutes for a full charge) x 100 gives approximately 45%.

The question is asking about the percentage charge of Kanna's DS after being charged for a specific period. First, we need to know how long it takes for a DS to become fully charged, which is 4 hours (equivalent to 240 minutes). Now, Kanna let her DS charge for 108 minutes, and the proportion of time spent charging to the total time needed to fully charge the DS represents the percentage of charge.

So, to calculate this, we would divide the time spent charging (108 minutes) by the total time needed for a full charge (240 minutes) and multiply by 100 to get the percentage.

Therefore, the calculation would be: (108/240) x 100 = 45% (rounding to the nearest whole number).

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Answer:

v(b)   = 4,5  mil/h      speed of the barge in still water

Step-by-step explanation:

d = v*t      barge going upstream       12 miles  and 4 hours trip

                barge returning back         12 miles  and 2 hours trip

let call   v(b) barge velocity   and

v(w)   water velocity

d  =  12 (Mil)  =  4 (h)* [(v(b) - v(w)]

  3   =  v(b)  - v(w)       (1)

d  =  12 (mil)  =  2 (h) * [ (v(b) + v(w)]

        6     =   v(b) + v(w)   (2)

Equations (1)  and (2)  is a two system equation. Solving

      from equation  (1)     v(w)  =  v(b)  - 3

By subtitution in equation (2)

         6   =  v(b)  + v(b)  - 3

         9   =  2v(b)

   v(b)   =  9/2      ⇒     v(b)   = 4,5  mil/h

Answer:

correct option is D. 54

Step-by-step explanation:

given data

product of digits = 210

integers = 10000

to find out

How many positive integers less than 10,000

solution

we know product of digits 210 are = 1 × 2× 3×5×7

210 = 1 × 6 × 5 × 7

here 2 × 3 = 6 ( only single digit )

here 4 digit numbers with combinations of the digits are = {1,6,5,7} and {2,3,5,7}

3 digit numbers with combinations of digits are = {6,5,7}

and product of their digits =  210

so combination will be

combinations of {1,6,5,7} is  4! = 4 × 3 × 2 × 1 =   24

combinations of {2,3,5,7}  is 4! =  4 × 3 × 2 × 1 = 24

combinations of {6,5,7} is 3! = 3 × 2 × 1 =  6

so total is = 24 + 24 + 6

total is = 54

so correct option is D. 54

Answer:

Explanation:

a). Description of what Brian did wrong.

Brian did not solve the inequality correctly. It seems he made several wrong steps:

b). Your work solving the inequality:

        - x < 3 - 2

        -x < 1

       x > - 1

Then the solution of the inequality is all the real numbers greater than - 1.

c). The correct solution graphed on a number line

d). The correct solution in set notation.

Three valid forms indicating the solution in set notation are:

Both the colon (:) and the straight bar (|) mean "such that".

Answer:

Step-by-step explanation:

This is one of the more interesting motion problems I've seen.  I like it!  If Kelly is driving north (straight up) for 9 miles, then turns east (right) and drives for 12 miles, what we have there are 2 sides of a right triangle.  The hypotenuse is created by Brenda's trip, which originated from the same starting point as Kelly and went straight to the destination, no turns.  We need the distance formula to solve this problem, so that means we need to find the distance that Brenda drove.  Using Pythagorean's Theorem:

[tex]9^2+12^2=c^2[/tex] and

[tex]81+144=c^2[/tex] and

[tex]225=c^2[/tex] so

c = 15.

Brenda drove 15 miles.  Now we can fill in a table with the info:

                d        =        r        x        t

Kelly     12+9               42                t

Brenda    15                45                t

Because they both left at the same time, t represents that same time, whatever that time is.  That's our unknown.

If d = rt, then for Kelly:

21 = 42t

For Brenda

15 = 45t

Solve Kelly's equation for t to get

t = 1/2 hr or 30 minutes

Solve Brenda's equations for t to get

t = 1/3 hr or 20 minutes

That means that Brenda arrived at the destination 10 minutes sooner than Kelly.

Answer:

the individual price of a popcorn is $8.

Step-by-step explanation:

p+2d=14 is the price with deal

p+2d=14+4 if there was no deal

plug 5 into the equation as d

2(5)+p=18

solve for p.

p=8

YOU GUYS GET NO MOM GET MO DAD GET MO GRANDMA GET NO GRANDPA GET NO CAR GET MO HOUSE…..your mom

Answer:

  a.  -1/18

Step-by-step explanation:

Differentiating implicitly, you have ...

  y^2 +2xyy' -2y' +12y^2y' = 0

Solving for y', we get ...

  y'(2xy -2 +12y^2) = -y^2

  y' = -y^2/(2xy -2 +12y^2)

To make use of this, we need to know the value of x at y=1. Filling in y=1 into the given equation, we have ...

  x -2 +4 = 6

  x = 4 . . . . . . . . subtract 2

So, at the point (x, y) = (4, 1), the slope is ...

  y' = -1/(8 -2 +12)

  y' = -1/18

_____

The attached graph shows that the line with slope -1/18 appears to be tangent to the curve at (4, 1).

Answer:

a) [tex]P(X=10)=(100C10)(0.127)^{10} (1-0.127)^{100-10}=0.0928[/tex]

b) [tex]P(X \leq 10) = 0.2614[/tex]

c) [tex] (1-0.127)^7 (0.127) =0.0491[/tex]

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

[tex]X \sim Binom(n=100, p=0.127)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

a. What is the probability that you count exactly 10 in poverty?

For this case we want this probability P(X=10)

[tex]P(X=10)=(100C10)(0.127)^{10} (1-0.127)^{100-10}=0.0928[/tex]

b. What is the probability that you count 10 or less in poverty?  .2614

For this case we want this probability [tex]P(X=\leq10)[/tex]

[tex]P(X\leq10)=P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)[/tex]

And we can find the individual probabilities like this:

[tex]P(X=0)=(100C0)(0.127)^{0} (1-0.127)^{100-0}=1.263x10^{-6}[/tex]

[tex]P(X=1)=(100C1)(0.127)^{1} (1-0.127)^{100-1}=1.837x10^{-5}[/tex]

[tex]P(X=2)=(100C2)(0.127)^{2} (1-0.127)^{100-2}=0.000132[/tex]

[tex]P(X=3)=(100C3)(0.127)^{3} (1-0.127)^{100-3}=0.000629[/tex]

[tex]P(X=4)=(100C4)(0.127)^{4} (1-0.127)^{100-4}=0.00222[/tex]

[tex]P(X=5)=(100C5)(0.127)^{5} (1-0.127)^{100-5}=0.00620[/tex]

[tex]P(X=6)=(100C6)(0.127)^{6} (1-0.127)^{100-6}=0.0143[/tex]

[tex]P(X=7)=(100C7)(0.127)^{7} (1-0.127)^{100-7}=0.0279[/tex]

[tex]P(X=8)=(100C8)(0.127)^{8} (1-0.127)^{100-8}=0.0471[/tex]

[tex]P(X=9)=(100C9)(0.127)^{9} (1-0.127)^{100-9}=0.0701[/tex]

[tex]P(X=10)=(100C10)(0.127)^{10} (1-0.127)^{100-10}=0.0928[/tex]

And then repplacing we got:

[tex]P(X \leq 10) = 0.2614[/tex]

c. What is the probability that you start taking the random sample and you find the first person in poverty on the 8th person selected?  .0491

For this case we need after 7 people , 1 in poverty so we can find this probability like this:

[tex] (1-0.127)^7 (0.127) =0.0491[/tex]

To calculate the probabilities, we can use the binomial probability formula. For part (a), the probability of counting exactly 10 people below the poverty level can be found by substituting the values into the formula. For part (b), the question is incomplete, so a specific answer cannot be provided.

To calculate the probabilities, we can use the binomial probability formula:

P(X=k) = C(n,k) * p^k * q^(n-k)

where:

- P(X=k) is the probability of getting exactly k successes

- C(n,k) is the number of ways to choose k items from a set of n items (combination)

- p is the probability of success

- q is the probability of failure (1-p)

In this case, we're interested in finding the probability of counting exactly 10 people living below the poverty level from a sample of 100 Americans, assuming the poverty rate is 12.7%.

To find the probability that exactly 10 people live below the poverty level, we have:

P(X=10) = C(100,10) * (0.127)^10 * (1-0.127)^(100-10)

Using a calculator or combinatorial calculator, we can find that C(100,10) = 17310309456440.

Substituting the values, we have:

P(X=10) = 17310309456440 * (0.127)^10 * (0.873)^90

Calculating this expression gives us the probability of counting exactly 10 people in poverty.

The question appears to be incomplete as it ends with 'you find'. Please provide the complete question for a more accurate answer.

Answer:

The estimated weight is in the range:

75.6 pounds [tex]\leq[/tex] Weight [tex]\leq[/tex] 92.4 pounds

Step-by-step explanation:

Since, the maximum error is 10%.

Therefore, the maximum and minimum vales will be 10% more and 10% less than 84 pounds, respectively.

For Maximum Limit:

[tex]Weight_{max}[/tex] = (1.1)(84 pounds)

[tex]Weight_{max}[/tex] = 92.4 pounds

For Minimum Limit:

[tex]Weight_{min}[/tex] = (0.9)(84 pounds)

[tex]Weight_{min}[/tex] = 75.6 pounds

Hence, the estimated weight is in the range:

75.6 pounds [tex]\leq[/tex] Weight [tex]\leq[/tex] 92.4 pounds

Answer:

The population of Shanghai is 5 times larger than population of Monterrey.

Step-by-step explanation:

Given:

The population of Monterrey, Mexico is [tex]4\times10^6[/tex] people

The population of Shanghai, China is [tex]2\times10^7[/tex] people.

To find how many times the population of Shanghai is lager than Monterrey.

Solution:

In order to find how many times the population of Shanghai is lager than Monterrey we will find the ratio of populations of Shanghai and  Monterrey.

Thus we divide the population of Shanghai by the population of Monterrey to find how many time the population of Shanghai is larger.

Thus, we have:

[tex]\frac{2\times10^7}{4\times10^6}[/tex]

Simplifying by using properties of exponents.

⇒ [tex]\frac{2\times10^{(7-6)}}{4}[/tex]  [As [tex]\frac{a^x} ]{a^y}=a^{(x-y)}[/tex]

⇒ [tex]\frac{2\times10^{(1)}}{4}[/tex]

⇒ [tex]\frac{20}{4}[/tex]

⇒ [tex]5[/tex]

Thus, we can say that the population of Shanghai is 5 times larger than population of Monterrey.

Shanghai's population is 5 times larger than Monterrey's.

To find out how many times larger the population of Shanghai is compared to Monterrey, we need to divide the population of Shanghai by the population of Monterrey.

Population of Shanghai: 2x[tex]10^7[/tex] people

Population of Monterrey: 4x[tex]10^6[/tex] people

Now, divide the population of Shanghai by the population of Monterrey:

[tex]2x10^7[/tex] / 4x[tex]10^6[/tex] = (2 / 4) x 10(7-6)

This simplifies to:

0.5 x 101 = 5

Therefore, the population of Shanghai is 5 times larger than the population of Monterrey.

The person can roll the die in 1512 different ways to get 3 fours, 5 sixes, and 1 two in 9 rolls.

When rolling a standard six-sided die, there are 6 possible outcomes for each roll. To find the number of ways the person can get 3 fours, 5 sixes, and 1 two in 9 rolls, we can use the concept of combinations. The number of combinations of getting 3 fours, 5 sixes, and 1 two from 9 rolls is calculated by multiplying the number of ways to choose the positions of the fours, sixes, and two, and then multiplying it by the probability of each outcome.

To calculate this, we can use the formula for combinations:

C(n, r) = n! / ((n - r)! x r!)

Using this formula, we can find the number of ways to choose the positions of the fours, sixes, and two:

Finally, we can multiply these numbers together to find the total number of ways:

Total number of ways = 84 x 6 x 3 = 1512

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Answer:80 mirror tiles will be needed to cover the wall is 80

Step-by-step explanation:

The dimension of one wall in living room is 8 feet by 10 feet. The wall is rectangular in shape. The area of a rectangle is expressed as

Length × width. The area of one wall in the living room would be

8 × 10 = 80 feet^2

The Williams family wants to cover one wall in their living room with 1-foot square mirror tiles.

The number of mirror tiles that they will need to cover the wall would be

80/1 = 80 mirror tiles.

The Williams family will need 80 mirror tiles to cover the wall.

The Williams family wants to cover one wall in their living room with 1-foot square mirror tiles. The wall measures 8 feet by 10 feet. To find out how many mirror tiles are needed, we calculate the area of the wall using the formula for area:

Area = length × width

Substituting the given measurements:

Area = 8 feet × 10 feet = 80 square feet

Since each mirror tile covers 1 square foot, the number of mirror tiles required is equal to the area of the wall:

Number of mirror tiles = 80

Therefore, the Williams family will need 80 mirror tiles to cover the wall.

Answer:

0.756

Step-by-step explanation:

It is given that a machine has four components, A, B, C, and D.

[tex]P(A)=P(B)=0.93, P(C)=0.95,P(D)=0.92[/tex]

If these components set up in such a manner that all four parts must work for the machine to work properly.

We need to find the probability that the machine works properly. It means we have to find the value of [tex]P(A\cap B\cap C\cap D)[/tex].

If two events X and Y are independent, then

[tex]P(X\cap Y)=P(X)\times P(Y)[/tex]

Assume the probability of one part working does not depend on the functionality of any of the other parts.

[tex]P(A\cap B\cap C\cap D)=P(A)\times P(B)\times P(C)\times P(D)[/tex]

Substitute the given values.

[tex]P(A\cap B\cap C\cap D)=0.93\times 0.93\times 0.95\times 0.92[/tex]

[tex]P(A\cap B\cap C\cap D)=0.7559226[/tex]

[tex]P(A\cap B\cap C\cap D)\approx 0.756[/tex]

Therefore, the probability that the machine works properly is 0.756.

Final answer:

The probability that the machine works properly is found by multiplying the probabilities of all four components working: P(A) * P(B) * P(C) * P(D) = 0.93 * 0.93 * 0.95 * 0.92 = 0.7513, or 75.13%.

Explanation:

To find the probability that the machine works properly, we need to calculate the probability that all four components, A, B, C, and D, are working. Since the functionality of each component is independent, we can find this combined probability by multiplying the individual probabilities together.

The probability of A working is P(A) = 0.93, B working is P(B) = 0.93, C working is P(C) = 0.95, and D working is P(D) = 0.92. So the probability of the machine working is:

P(Machine works) = P(A) * P(B) * P(C) * P(D) = 0.93 * 0.93 * 0.95 * 0.92 = 0.7513

Therefore, the probability that the machine works properly is 0.7513, which is 75.13%.

Answer:

Required equation : [tex]\frac{1}{t}=\frac{1}{3}+\frac{1}{9}[/tex]

Together they can paint the same room in 2.25 hours or 2 hours 15 minutes.

Step-by-step explanation:

It is given that Dale Horton can paint a certain room in 3 hours.

One hour woks of Dale Horton = 1/3

Kathy Garcia can paint the same room in 9 hours.

One hour woks of Kathy Garcia = 1/9

Let together they can paint the same room in t hours.

One hour woks of both = 1/t

[tex]\frac{1}{t}=\frac{1}{3}+\frac{1}{9}[/tex]

[tex]\frac{1}{t}=\frac{3+1}{9}[/tex]

[tex]\frac{1}{t}=\frac{4}{9}[/tex]

After reciprocal we get

[tex]\frac{t}{1}=\frac{9}{4}[/tex]

[tex]t=2.25[/tex]

1 hour = 60 minutes.

0.25 hour = 15 minutes.

Therefore, together they can paint the same room in 2.25 hours or 2 hours 15 minutes.

Answer:

A) 15 < x < 24

Step-by-step explanation:

According to the law of the triangle, we know that the lengths of any two sides of a triangle are more significant than the length of the 3rd side. Here A is the answer because 15 is the length of the first side, and 39 is the length of the third side. So the length of the 2nd side is (39-15) = 24. It means that the length of the 2nd side is included between 15<x<24.

Question is not proper, Proper question is given below;

For a birthday party, Mr. Perkins orders 8 chocolate chip cookies and 16 sugar cookies. Each cookie is the same price. He also picks up a cupcake for himself, which costs $2.75. The total bill is $44.03. What is the cost of a cookie?

Answer:

The Cost of the cookie will be $1.72.

Step-by-step explanation:

Given:

Mr Perkins orders 8 chocolate chip cookies and 16 sugar cookies.

Since cost of both the cookies are same then Let us assume the cost of cookies be 'x'.

Total cost of the cookies = [tex](8 + 16)x = 24x[/tex]

Cost of Cup cakes = $2.75.

Total bill he pays = $44.03

We need to find the cost of each cookies.

Now we know that Total bill he pays is equal to sum of Cost of cookies and Cost of Cup cakes he bought.

Framing in equation form we get;

[tex]44.03 = 24x + 2.75[/tex]

Now Subtracting both side by 2.75 using Subtraction property we get;

[tex]2.75+24x-2.75 = 44.03 - 2.75\\\\24x = 41.28[/tex]

Now Dividing both side by 24 using Division property we get;

[tex]\frac{24x}{24} = \frac{41.28}{24}\\\\x=1.72[/tex]

Hence The Cost of the cookie will be $1.72.

Answer:

option D

Step-by-step explanation:

Assume number of bulb in the hostel be 100

number of bulb on at 8 p.m.

           = 80 % of total bulb

           = 0.8 x 100 = 80 bulb

Let L be the number of light on and 100 - L be the light that are off

now,

Light on = 40 % of (100 - L) + 90 % of L

80 = 40 - 0.4 L + 0.9 L

40 = 0.5 L

 L = 80 bulb

number of bulbs which were off = 100-80 = 20 bulb

number of bulbs that are on are supposed to be off =  40 % of 20

                = 0.4 x 20 = 8 bulbs

percentage = [tex]\dfrac{8}{80}}\times 100[/tex]

                   = 10 %

Hence, the correct answer is option D

Answer:

The correct answer is B. 3 to 2.

Step-by-step explanation:

To solve this problem let suppose

English = E

History = H

Maths = M

so

E = H* 2 (there are twice as many English majors as history majors)

E = M* 3 (three times as many English majors as mathematics majors)

lets suppose E=6 then,

H = 3 and M =2

So

H to M = 3/2.

Using algebra, we establish that if the number of mathematics majors is x, then the number of English majors is 3x and history majors would be 3x/2. The ratio of history majors to mathematics majors simplifies to 3:2.

To determine the ratio of the number of history majors to the number of mathematics majors given the provided relationships among different majors, we must set up the problem with algebra. Let's assume the number of mathematics majors is x. According to the problem, there are three times as many English majors as mathematics majors, so the number of English majors is 3x. It is also stated that there are twice as many English majors as history majors. Since the number of English majors is 3x, the number of history majors must be 3x/2.

Now, we establish the ratio of history majors to mathematics majors using the numbers we have. Since we have 3x/2 for history majors and x for mathematics majors, we can write the ratio as (3x/2):x which simplifies to 3:2 since x cancels out in the ratio.

Therefore, the correct answer is B. 3 to 2.

To find the number of two-bedroom and three-bedroom units in the complex, we can set up a system of equations and solve them using substitution or elimination.

To solve this problem, we need to set up a system of equations. Let x represent the number of two-bedroom units and y represent the number of three-bedroom units. From the problem, we know that there are a total of 195 condos. So, we have the equation: x + y = 195. We also know that the total number of bedrooms is 497, which can be expressed as: 2x + 3y = 497. We can now solve this system of equations using substitution or elimination to find the values of x and y. When solved, we find that there are 112 two-bedroom units and 83 three-bedroom units in the complex.

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Answer:

Therefore, ( 1 , 1 ) is the Solution to the Given Equations

[tex]y=2x-1[/tex]  

[tex]5x-4y=1[/tex]

Step-by-step explanation:

Given:

[tex]y=2x-1[/tex]   ..............Equation ( 1 )

[tex]5x-4y=1[/tex] ..............Equation ( 2 )

To Find:

x = ?

y = ?

Solution:

[tex]y=2x-1[/tex]   ..............Equation ( 1 )

[tex]5x-4y=1[/tex] ..............Equation ( 2 )

Substituting equation 1 in equation 2 we get

[tex]5x-4(2x-1)=1\\applying\ distributive\ property\ we\ get\\5x-8x+4=1\\\\-3x=1-4=-3\\\\x=\frac{-3}{-3}=1\\ \therefore x = 1\\[/tex]

Substituting 'x' in Equation ( 1 ) we get

[tex]y=2\times 1-1\\\\y=1\\\\\therefore y =1\\[/tex]

Therefore, ( 1 , 1 ) is the Solution to the Given Equations

[tex]y=2x-1[/tex]  

[tex]5x-4y=1[/tex]

Answer:The number of the 2- pound bags is 56 and the number of the 5- pound bags is 140

Step-by-step explanation:

Let the number of the 2- pound bags and the 5- pound bags be n since they used the same number.

5n + 2n = 196

7n=196

n= 196/7

n= 28

Therefore the number of the 2- pound bags is 2× 28= 56

and the number if the 5- pound bags is 5×28= 140

First, convert the APR to the periodic interest rate by dividing it by the number of compounds in a year. Then, determine the number of periods by multiplying the number of years by the number of compounds per year. Finally, use these values in the compound interest formula to find the balance.

To solve this, we first need to switch from Annual Percentage Rate (APR) to the periodic interest rate. APR is an annual measure, but interest is compounded quarterly in this case. The periodic interest rate is the APR divided by the number of compounds in a year. So 2.6% APR converted to a periodic interest rate is 0.026/4 = 0.0065.

Next we determine the total number of periods. Since we have 6 years and interest is compounded quarterly, we have 4 compounds/year * 6 years = 24 periods.

Now we can use the compound interest formula: A=P(1+r/n)^(nt), where:

Substitute these values into the formula, we get: A = 3200(1 + 0.0065)^(24), calculate this to get the balance.

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The probabilities are (a) the probability that both balls are white is 0.058 and (b) the probability that both balls are the same color is 1.904.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

A bowl contains 6 red balls, 4 blue balls, 3 white balls and 1 green ball. You pick two balls without replacement.

Total number of balls : 6+4+3 +1 = 13

(a)

Out of 13 balls,

3 are white, so probability of getting first white ball is,

P(first white) = 3/13

After that 12 balls remaining out of which 3 are white so

P(second white| first white) = 3/12

So required probability is

P(both white) = P(Second white| first white)P(first white) = (3/13) x (3/12) = 0.0576 = 0.058

(b)

Since there is only one green ball, so both balls cannot be same. Therefore,

P(both of same color) = P(both blue)+P(both red)+P(both white) = 0.923+ 0.923+ 0.058= 1.904

The probability that both balls of same color is

P(both of same colors) = 1.904

Therefore, the probabilities are (a) 0.058 and (b) 1.904

To learn more about the probability;

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√57 = 7.549

Round to 7.5

Answer:

7.5

Step-by-step explanation:

7.549

Answer:YES

Step-by-step explanation:

Answer : Yes, regular and sale prices represent a proportional relationship.

Step-by-step explanation :

We have to determine the ratio of regular and sale prices of shirt, jeans and boots .

A shirt was originally $9.50 and now is $7.60.

[tex]\frac{\text{Regular price}}{\text{Sale price}}=\frac{\$ 9.50}{\$ 7.60}[/tex]

[tex]\frac{\text{Regular price}}{\text{Sale price}}=\frac{5}{4}[/tex]

A pair of jeans were $25.00, and now they are priced $20.00.

[tex]\frac{\text{Regular price}}{\text{Sale price}}=\frac{\$ 25.00}{\$ 20.00}[/tex]

[tex]\frac{\text{Regular price}}{\text{Sale price}}=\frac{5}{4}[/tex]

A pair of boots were $55.00, and they are on sale for $44.00.

[tex]\frac{\text{Regular price}}{\text{Sale price}}=\frac{\$ 55.00}{\$ 44.00}[/tex]

[tex]\frac{\text{Regular price}}{\text{Sale price}}=\frac{5}{4}[/tex]

From this we conclude that, all the items are in same ratio that means the regular and sale prices represent a proportional relationship.

Hence, yes, regular and sale prices represent a proportional relationship.

Answer:

D because x is what you subtract/add to get zero in (x − 6). x - 6 + 6 = 0

That is how the class taught me.