please simplify this

Answer:

Hey there!

We have x+2y=5, and x-2y=5.

x+2y=5

x-2y=5

Add the x's to get 2x and the 2y's to get 0. Finally add the 5's to get 10.  

Thus, we have 2x+0=10, or 2x=10.

x=5

y=0

Hope this helps :)

Answer:

x=3,y=1

Step-by-step explanation:

x+2y = 5

x-2y = 1

Add the two equations together to eliminate y

x+2y = 5

x-2y = 1

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

2x +0y = 6

Divide by 2

2x/2 = 6/2

x = 3

Then solve for y

x+2y = 5

3 + 2y =5

2y = 5-3

2y = 2

Divide by 2

2y/2 = 2/2

y =1

x=3,y=1

Check

3+2(1) = 5

5=5

3-2(1)=1

1=1

Answer:

x=3, y=-2, z=1

Step-by-step explanation:

I solved by substitution

Answer:

x = 3; y = -2; z = 1.

Step-by-step explanation:

-x + 2y + 4z = -3

x – 2y - 3z = 4

(-x + x) + (2y - 2y) + (4z - 3z) = (-3 + 4)

0 + 0 + z = 1

z = 1

x - 2y - 3(1) = 4

x - 2y - 3 = 4

x - 2y = 7

x = 2y + 7

2(2y + 7) + y - (1) = 3

4y + 14 + y - 1 = 3

5y + 13 = 3

5y = -10

y = -2

x = 2(-2) + 7

x = -4 + 7

x = 3

So, your answer is (3, -2, 1).

Hope this helps!

Answer:

1) We have to multiply both sides by  1/(de)

2) c=ab/(cd)

Step-by-step explanation:

We have to achieve the right side expression be c only.  To do that we have to multiply cde by   1/(de) .  However we have to multiply the left side by

1/(de) as well.

So the resulting left side expression is:

ab *1/(de)=ab/(de)

So c= ab/(de)

Given equation in the question is,

ab = cde

To solve the given equation for the value of c, follow the algebraic rules,

1). Multiply both the sides of the equation with [tex]\frac{1}{de}[/tex],

   [tex]ab\times \frac{1}{de} = \frac{cde}{de}[/tex]

   [tex]\frac{ab}{de}= \frac{cde}{de}[/tex]

   [tex]\frac{ab}{de}=c[/tex]

Therefore, resulting equation for c will be,

[tex]c=\frac{ab}{de}[/tex]

Learn more,

https://brainly.com/question/11496615

Answer:

A repeating decimal is not a rational number and The product of two irrational numbers is always rational

Step-by-step explanation:

One statement that is not true is "The product of two irrational numbers is always rational". Take for example the irrational numbers √2 and √3. Their product is √6 which is also irrational.

The other false statement is "A repeating decimal is not a rational number". Take for example the repeating decimal 0.33333..... It can be written as 1/3 which is a rational number.

Answer:

12 batches of scones

Explanation:

3/0.25=3*4=12

Answer:

The functions that represent this situation are A. [tex]f(n)=3\cdot 2^{n-1}[/tex] and C. [tex]a(n)=a(n-1)\cdot 2; a(1)=3[/tex].

Step-by-step explanation:

A geometric sequence goes from one term to the next by always multiplying or dividing by the same value.

In geometric sequences, the ratio between consecutive terms is always the same. We call that ratio the common ratio.

This is the explicit formula for the geometric sequence whose first term is k and common ratio is r:

                                                [tex]a(n)=k\cdot r^{n-1}[/tex]

This is the recursive formula of that sequence:

                                                 [tex]a(1)=k\\\\a(n)=a(n-1)\cdot r[/tex]

We know that the first term is k = 3 and the common ratio is r = 2. Therefore,

The explicit formula is [tex]f(n)=3\cdot 2^{n-1}[/tex] and the recursive formula is [tex]a(n)=a(n-1)\cdot 2; a(1)=3[/tex].

Answer:

a) Check Explanation

b) Probability that 11 out of the 17 randomly selected flights are on time = P(X = 11) = 0.0680

c) Probability that fewer than 11 out of the 17 randomly selected flights are on time

= P(X < 11) = 0.0377

d) Probability that at least 11 out of the 17 randomly selected flights are on time

= P(X ≥ 11) = 0.9623

e) Probability that between 9 and 11 flights, inclusive, out of the randomly selected 17 are on time = P(9 ≤ X ≤ 11) = 0.1031

Step-by-step explanation:

a) How to know a binomial experiment

1) A binomial experiment is one in which the probability of success doesn't change with every run or number of trials. (Probability of each flight being on time is 80%)

2) It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure. (It's either the flights are on time or not).

3) The outcome of each trial/run of a binomial experiment is independent of one another.

All true for this experiment.

b) Probability that exactly 11 flights are on time.

Let X be the random variable that represents the number of flights that are on time out of the randomly selected 17.

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 17 randomly selected flights

x = Number of successes required = number of flights required to be on time

p = probability of success = Probability of a flight being on time = 80% = 0.80

q = probability of failure = Probability of a flight NOT being on time = 1 - p = 1 - 0.80 = 0.20

P(X = 11) = ¹⁷C₁₁ (0.80)¹¹ (0.20)¹⁷⁻¹¹ = 0.06803777953 = 0.0680

c) Probability that fewer than 11 flights are on time

This is also computed using binomial formula

It is the probability that the number of flights on time are less than 11

P(X < 11) = P(X = 0) + 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) = 0.0376634429 = 0.0377

d) Probability that at least 11 out of the 17 randomly selected flights are on time

This is the probability of the number of flights on time being 11 or more.

P(X ≥ 11) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17)

= 1 - P(X < 11)

= 1 - 0.0376634429

= 0.9623365571 = 0.9623

e) Probability that between 9 and 11 flights, inclusive, are on time = P(9 ≤ X ≤ 11)

This is the probability that exactly 9, 10 or 11 flights are on time.

P(9 ≤ X ≤ 11) = P(X = 9) + P(X = 10) + P(X = 11)

= 0.0083528524 + 0.02672912767 + 0.06803777953

= 0.1031197592 = 0.1031

Hope this Helps!!!

Answer:

a) The normal distribution function for the IQ of a randomly selected individual is presented in the first attached image to this solution.

b) The probability that the person has an IQ greater than 105 = P(X > 105) = 0.3707

The sketch of this probability is presented in the second attached image to this solution.

c) The minimum IQ needed to qualify for the Mensa organization = 130.81. Hence, P(X > 131) = 2%

The sketched image of this probability is presented also in the second attached image to the solution. The shaded region is the required probability.

d) The middle 40% of IQs fall between 92 and 108 IQ respectively.

P(x1 < X < x2) = P(92 < X < 108) = 0.40

The sketched image of this probability is presented in the third attached image to the solution. The shaded region is the required probability.

Step-by-step explanation:

The IQ of an individual is given as a normal distribution withh

Mean = μ = 100

Standard deviation = σ = 15

If X is a random variable which represents the IQ of an individual

a) The distribution of X will then be given as the same as that of a normal distribution.

f(x) = (1/σ√2π) {e^ - [(x - μ)²/2σ²]}

The normal distribution probability density function is more clearly presented in the first attached image to this question

b) Probability that the person has an IQ greater than 105.

To find this probability, we will use the normal probability tables

We first normalize/standardize 105.

The standardized score of any value is that value minus the mean divided by the standard deviation.

z = (x - μ)/σ = (105 - 100)/15 = 0.33

P(x > 105) = P(z > 0.33)

Checking the tables

P(x > 105) = P(z > 0.33) = 1 - P(z ≤ 0.33) = 1 - 0.6293 = 0.3707

The sketch of this probability is presented in the second attached image to this question. The shaded region is the required probability.

c) Mensa is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the Mensa organization.

We need to find x for P(X > x) = 2% = 0.02

Let the corresponding z-score for this probability be z'

P(X > x) = P(z > z') = 0.02

P(z > z') = P(z ≤ z') = 1 - 0.02 = 0.98

From the normal distribution table, z' = 2.054

z = (x - μ)/σ

2.054 = (x - 100)/15

x = 2.054×15 + 100 = 130.81 = 131 to the nearest whole number.

The sketched image of this probability is presented also in the second attached image to the solution. The shaded region is the required probability.

d) The middle 40% of IQs fall between what two values?

P(x1 < X < x2) = 0.40

Since the normal distribution is symmetric about the mean, the lower limit of this IQ range will be greater than the lower 30% region of the IQ distribution and the upper limit too is lesser than upper 30% region of the distribution.

P(X < x1) = 0.30

P(X > x2) = 0.30, P(X ≤ x2) = 1 - 0.30 = 0.70

Let the z-scores of x1 and x2 be z1 and z2 respectively.

P(X < x1) = P(z < z1) = 0.30

P(X ≤ x2) = P(z ≤ z2) = 0.70

From the normal distribution tables,

z1 = -0.524

z2 = 0.524

z1 = (x1 - μ)/σ

-0.524 = (x1 - 100)/15

x1 = -0.524×15 + 100 = 92.14 = 92 to the nearest whole number.

z2 = (x2 - μ)/σ

0.524 = (x2 - 100)/15

x2 = 0.524×15 + 100 = 107.86. = 108 to the nearest whole number.

The sketched image of this probability is presented in the third attached image to the solution. The shaded region is the required probability.

Hope this Helps!!!

Answer:

Step-by-step explanation:

To solve for x we use sine

sin ∅ = opposite / hypotenuse

From the question

38 is the hypotenuse

20 is the opposite

So we have

sin x = 20/38

sin x = 10/19

x = sin-¹ 10/19

x = 31.75

Hope this helps you

Answer:

A

Step-by-step explanation:

Answer:

The Empirical Rule

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed(bell-shaped) random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

So the answer to this question is the Empirical Rule

Answer:

3

Step-by-step explanation:

Hey there! :)

Answer:

n = 12.

Step-by-step explanation:

Given:

5/6n = 10

Solve by isolating the variable. Divide both sides by 5/6. (Multiply by the reciprocal)

5/6n · 6/5 = 10 · 6/5

n = 10 · 6/5

n = 12.

Answer:

6n = 10 ×5

6n = 50

n = 50/6

n = 8.3

Answer:  C) -98, -686, -4,802, -33,614

Step-by-step explanation:

There are 5 steps from -14 to -235,298.

First, let's find the ratio (r):

[tex]-14r^5=-235,298\\\\r^5=\dfrac{-235,298}{-14}\\\\r^5=16,807\\\\r=\sqrt[5]{16,807} \\\\r=7[/tex]

Next, multiply each term by r = 7

-14 x 7 = -98

             -98 x 7 = -686

                            -686 x 7 = -4,802

                                             -4,802 x 7 = -33,614

                                                                  -33,614 x 7 = -235,298 [tex]\checkmark[/tex]

4. 12 cent

5. $2.06

6. $1.56

7. $1.30

8. 86 cent

Answer:

The sales for the store 7 days after the end of the advertising campaign is  

          [tex]G_7 =[/tex]$3849.74

Step-by-step explanation:

From the question we are told that

    The daily sales on the end of campaign day is  [tex]G_o[/tex] =  $8,500

     The  daily sales three days after end of campaign day is  [tex]G_3[/tex] = $ 5,100

     The  usual day sales of the store is [tex]G_u[/tex]  =  $ 3,500

Generally the Newton's Law of Cooling (Heating). equation is  mathematically represented as

         [tex]G_t = G_u+ [(G_o -S_u ) * e^{-(k*t)}][/tex]

Here t is the number of day after the campaign ended

Now substituting values to obtain the constant k

For  t =  3

         [tex]G_3 = G_u + [(G_o -S_u ) * e^{-(k*3)}][/tex]

          [tex]5100 = 3500 [(8500 -3500 ) * e^{-(k*3)}][/tex]

         [tex]e^{-(k*3)} = 0.32[/tex]

=>     [tex]-3k = ln (0.6)[/tex]

=>      [tex]-3k = -1.1394[/tex]

=>        [tex]k = 0.380[/tex]

So at  t =  7

     [tex]G_7 = G_u + [(G_o -S_u )] * e^{-(k*7)}[/tex]

substituting values

    [tex]G_7 = 3500 + [(8500 -3500 )] * e^{-(0.3780*7)}[/tex]

    [tex]G_7 =[/tex]$3849.74

This question is incomplete because the options are missing; here is the question statement and options:

To improve the logical flow of the paragraph, the best place to move sentence 7 is before

A. Sentence 1.

B. Sentence 3.

C. Sentence 5.

D. Sentence 6.

The correct answer is B. Sentence 3

Explanation:

The paragraph develops an argument through different sections. This includes the thesis statement "schools should switch from using paper textbooks to using computer tablets", reasons and evidence that support this thesis, the explanation of one counterclaim, and finally, reasons to disprove the counterclaim and confirm the claim.

In the case of sentence 7 "Many experts agree that switching to tablets is  important for the future of education" this provides a reason that supports the argument and due to this, it is more appropriate this sentence is placed after the thesis and before the counterclaim "Opponents argue that tablets ...".

In this context, this sentence should be placed before sentence 3 that belongs to the evidence provided to support the claim. Moreover, sentence 7 would appropriately introduce sentence 3 as they are both related to the opinion of experts about this issue.

The 7th sentence can be placed before the first, third, and fifth.

The process of making an important decision is known as decision making.

Given

7 statement is there.

To find the position of the 7th sentence.

7th sentence can be placed before the first because it seems that the conversation is starting.

7th sentence can be placed before the third because you can say as an update will be done by  Federal Communications Commission.

7th sentence can be placed before the fifth because the secretary wants to implement it in his system due to its regular update.

Thus, the 7th sentence can be placed before the first, third, and fifth.

More about the decision-making link is given below.

https://brainly.com/question/3369578

Answer:

Ending inventory cost= $56,700

Step-by-step explanation:

Giving the following information:

Production costs (19,900 units):

Direct materials $172,700

Direct labor 221,400

Variable factory overhead 265,400

Fixed factory overhead 92,800

Total= $752,300

The absorption costing method includes all costs related to production, both fixed and variable. The unit product cost is calculated using direct material, direct labor, and total unitary manufacturing overhead.

Total unitary production cost= 752,300/19,900= $37.80

Units in ending inventory= 1,500

Ending inventory cost= 1,500*37.8

Ending inventory cost= $56,700

Answer:  any amount from 0 to 90000 USD

Step-by-step explanation:

x USD will be paid for 15% bonds that makes x*0.15 USD /per year

So 90000-x will be paid for 7% bonds , that makes (90000-x)*0.07 USD/per year= 6300-0.07x   USD / per year.

So the total amount the woman gets from both investments yearly should be not less than 3000 USD/per year

Otherwise

0.15*x+6300-0.07*x>=3000

0.08*x+6300>=3000

The inequation is correct for any x>=0

The woman will be able invest in CD any amount from 0 to 90000 USD.

If we suppose that investments in CD more safe we'd recommend to the lady to invest all money to CD.

Answer:

see below

Step-by-step explanation:

$3000 is not a right number or $90000

Assume n instead of $3000, then

is required equation

x= (n-6300)/0.08 is the amount invested in the 15% bond

Consider n> $6300

Then 90000 -x will be the amount invested in the CD

Answer:

b

Step-by-step explanation:

30/3x=10

Answer:

Volume of the sphere= 113.112 cubic inch(Inch ³)

Step-by-step explanation:

First of all the formula for the volume of a sphere Is given as 4πr³

Already the radius r is already given as 3 inches

While π = 3.142

Volume of the sphere = 4/3πr³

Volume of the sphere = 4/3(3.142)(3)³

Volume of the sphere= 4/3(3.142)(27)

Volume of the sphere= 4/3(84.834)

Volume of the sphere= 339.336/3

Volume of the sphere= 113.112 Inch ³

Volume of the sphere= 113.112 cubic inch

Answer:

The probability of the infected is more than 8 in a hour is 0.00384

Step-by-step explanation:

Given that the Mean of the arrival rate of the infect follows a Poisson distribution =   x`= 3 / hour

The Poisson distribution formula is given by

P(X) = e-ˣ` x`ˣ/ x!

The mean is 3 and we have to find the probability of 8 or more which means

1 -X  where X takes the values of 0,1,2,3,------,8.

P( more than 8 ) = 1- P( X ≤ 8 ) =1- {e-³ (3)⁸/8! +e-³ (3)⁷/7! +e-³ (3)⁶/6! +e-³ (3)⁵/5! +e-³ (3)⁴/4! +e-³ (3)³/3! +e-³ (3)²/2!+ e-³ (3)¹/1! +e-³ (3)⁰/0!}

Putting the Values

P( more than 8 ) = 1- P( X ≤ 8 ) =1- [ 0.04979*6561 / 40320 +0.04979*2187 / 5040 + 0.04979*729 / 720 +0.04979*243 / 120+0.04979*81 / 24 + 0.04979 *27 / 6 + 0.04979 *9 /2 + 0.04979*3/ 1 + 0.04979*1/1 }

Solving

P( more than 8 ) = 1- P( X ≤ 8 ) =1- [ 0.0081 + 0.0216 + 0.0504 + 0.1008 + 0.1680 + 0.2240 + 0.2241+ 0.14937 + 0.04979]

P( more than 8 ) = 1- P( X ≤ 8 ) =1-0.99616

P( more than 8 ) = 1- P( X ≤ 8 ) =0.00384

Answer: 9

Step-by-step explanation:

Apex

Answer:

2x-2

Step-by-step explanation:

2(x-1)=

Distribute

2x* -2*1

2x-2

Answer:

[tex]2x - 2[/tex]

Solution,

[tex]2(x - 1) \\ = 2 \times x - 2 \times 1 \\ = 2x - 2[/tex]

hope this helps..

Answer:

i-09 vhcgcdg hdc

Step-by-step explanation:

Answer:

12 - 12

Step-by-step explanation:

Given

Initial Temperature (at 12 midnight) = 12 deg C

By 6am; Temperature has decreased by 12 deg C

Required

What expression represents the situation

Provided that there was a decrement in the temperature; the system will b represented by Initial Temperature minus Change in temperature

Expression = Initial Temperature - Change in Temperature

Expression = 12C - 12C

Solving further to get the actual temperature at 6

Final Temperature = 12C - 12C

Final Temperature = 0 C

Answer:

12-12

Step-by-step explanation:

Step-by-step explanation:

1) x - 5 = - 2

x = - 2 + 5

x = 3

2) - 6 + x = - 9

x = - 9 + 6

x = - 3.

3) x/4 = 6/8

Cross multiply

8x = 24

x = 24/8 = 3

4) - 14x = - 42

x = - 42/-14

x = 3

5) - 3/5 + x = 12/5

x = 12/5 + 3/5

x = 15/5 = 3

6) x/3 = 9

x / 3 - 9

x - 3

x = 3

The solution is shown below:

A  statement of equality between two expressions consisting of variables and/or numbers

x=3                                                             x≠3

1) x - 5 = - 2                                             2) - 6 + x = - 9

x = - 2 + 5                                                       x = - 9 + 6

x = 3                                                                x = - 3.

3) x/4 = 6/8                                                6) x/3 = 9  

x = 24                                                               x = 27

x = 24/8

x = 3

4) - 14x = - 42

x = - 42/-14

x = 3

5) - 3/5 + x = 12/5

x = 12/5 + 3/5

x = 15/5

x = 3

Learn more about equation here:

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Answer:

a) This t-value obtained (2.92) is in the rejection region (t > 1.69), hence, the sample does not support the cofdee industry's claim.

b) p-value for this test = 0.006266

c) The p-value obtained for this test is lesser than the significance level at which the test was performed, hence, we can reject the nuĺl hypothesis and say that there is enough evidence to suggest that the coffee industry's claim isn't true based in results obtained from the sample data.

Step-by-step explanation:

a) Degree of freedom = n - 1 = 34 - 1 = 33

The critical value of t for a significance level of 0.10 and degree of freedom of 33 = 1.69

Since we are testing in both directions whether the the average U.S. adult drinks 1.7 cups of coffee per day using our sample,

The rejection region is t < -1.69 and t > 1.69

So, we compute the t-statistic for this sample data to test the claim.

t = (x - μ)/σₓ

x = sample mean = 1.95 cups of coffee per day

μ₀ = The standard we are comparing against = 1.7 cups of coffee per day

σₓ = standard error = (σ/√n)

σ = standard deviation = 0.5 cups

n = Sample size = 34

σₓ = (0.5/√34) = 0.0857492926 = 0.08575

t = (1.95 - 1.70) ÷ 0.08575

t = 2.9154759464 = 2.92

This t-value obtained is in the rejection region, hence, the sample does not support the cofdee industry's claim.

b) Checking the tables for the p-value of this t-statistic

Degree of freedom = df = n - 1 = 34 - 1 = 33

Significance level = 0.10

The hypothesis test uses a two-tailed condition because we're testing in both directions.

p-value (for t = 2.92, at 0.10 significance level, df = 33, with a two tailed condition) = 0.006266

c) To use PHStat, the claim that the average U.S. adult drinks 1.7 cups of coffee per day is the null hypothesis.

The alternative hypothesis is that the real number of cups of coffee that the average U.S. adult drinks as obtained from the sample data, is significantly different from the 1.7 in the coffee industry's claim.

The p-value obtained from PHstat = 0.0063

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.10

p-value = 0.0063

0.0063 < 0.10

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to suggest that the coffee industry's claim isn't true based in results obtained from the sample data.

Hope this Helps!!!

Answer:

x = 38

y =2

z=-1

Step-by-step explanation:

z = -1

Substituting into the second equation

y-z =3

y - -1 =3

y+1 = 3

Subtract 1

y+1-1= 3-1

y =2

Substituting into the first equation

x -2y +2z = 32

x -2(2) +2(-1) = 32

x-4-2 = 32

x-6 = 32

Add 6 to each side

x-6+6 =32+6

x = 38