complete the equation describing how x and y are related.

Answer: When the addition of two or more equations leads to the elimination of one of the variables.

Step-by-step explanation:

When we have a system of equations, the addition method seems to be useful only when adding the equations will lead to the elimination of one of the variables:

An example of this can be, for the variables x and y:

3*x + x*y - 2*y = 3

x^2 + x*y - 2y = 42

now we can "add" (actually subtract) the equations and get (eq2 minus eq1)

(x^2 + x*y - 2y) - (3*x + x*y - 2*y ) = 42 - 3

x^2 - 3*x = 39

x^2 - 3*x - 39 = 0

And now we can solve it for x, and then find the value of y.

Answer:

-1

Explanation:

Let the number be x.

Then the equation will be:

3(x+18) = 51

=> 3x + 54 = 51

=> 3x = 51 - 54

=> 3x = -3

=> x = -3/3

=> x = -1

So, the number you thought of is -1.

Answer:

The number is 3.

Step-by-step explanation:

[tex]3(14+x)=51\\42+3x=51\\3x=9\\x=3[/tex]

Answer:

2 + 109 = 111

Step-by-step explanation:

.............

Answer:

The author have to use his/her phone less than 20 hours in a month in order for Don’tTalkMuch's is a deal to be better than TalkLots's is.

Step-by-step explanation:

Call X is the number of hours that the author uses on monthly basis.

Total bill value if the author uses Don’tTalkMuch service is $80 + $1 X.

Total bill value if the author uses TalkLots service is $20 + $4X

The total fees between 2 providers equal as:

$80 + $1 X = $20 + $4X => 3X = $60 => X = 20

Hence: The author have to use his/her phone less than 20 hours in a month in order for Don’tTalkMuch's is a deal to be better than TalkLots's is.

Answer:

But the answer is 42

I did I got 42 .

:(

A = 1 and 8

B = 2 and 4

C = 2 and 7

I’m pretty sure this is right? I’m still learning too :p

=======================================================

Explanations:

For the sake of simplicity, imagine that lines m and n are parallel. They don't necessarily need to be in order to answer this problem, but it might help with the terminology better.

When we use the term "interior" we basically mean the region between or inside the parallel lines. So "exterior" is everything but that, which is composed of two separate regions that don't overlap. Exterior angles shown in this diagram are

angle 1, angle 5, angle 4, angle 8

The "alternate" refers to the idea that we're on alternate sides of the transversal cutting line. One pair of alternate exterior angles is angle 1 and angle 8. We have angle 1 below the transversal while angle 8 is on the opposite side and above the transversal. For similar reasoning, angles 5 and 4 are alternate exterior angles as well.

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

Notice how each line crosses to form an X shape, producing 4 angles that share the same common vertex point. For instance, angles 1, 5, 6 and 2 are all around the same point.

Angle 1 and angle 3 are corresponding angles because they

So in short, they are both in the same corner of each four corner angle configuration. They are both in the bottom left corner. This is the full list of all corresponding angle pairs

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

As stated in the first section above, the interior region is between the parallel lines. Alternate interior angles alternate being above and below the transversal line.

So this applies to angle 2 and angle 7. It also works for angle 3 and angle 6.

Answer:

Yes it is reasonable to conclude the mean rate charged is greater than 14%

Step-by-step explanation:

From the question we are told that

    The  population mean is  [tex]\mu = 0.14[/tex]

    The sample size is  [tex]n = 10[/tex]

    The  sample mean is  [tex]\= x = 0.1564[/tex]

     The  standard deviation is  [tex]\sigma = 0.01561[/tex]

     The level of significance is  [tex]\alpha = 0.01[/tex]

The null hypothesis is    [tex]H_o: \mu = 0.14[/tex]

The  alternative hypothesis is  [tex]H_a : \mu > 0.14[/tex]

 Generally the test statistic is mathematically represented as

              [tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

              [tex]t = \frac{ 0.1564 - 0.14 }{ \frac{0.01561 }{\sqrt{10} } }[/tex]

              [tex]t = 3.322[/tex]

Now the p-value obtained from the z-table is

        [tex]p-value = P(t > 3.322) = 0.00044687[/tex]

Since the [tex]p-value < \alpha[/tex] then we reject the null hypothesis, hence we can conclude that  the mean rate charged is greater than 14%

Answer:

  -864

Step-by-step explanation:

The determinant of a matrix product is the product of the determinants. The determinant of a transpose is the same as the determinant of the original. Hence ...

  [tex]|AB^5C^T|=(4)(-2)^5(\frac{1}{4})=-32[/tex]

The multiplication of an n×n matrix by a scalar 'a' multiplies its determinant by a^n, so the desired determinant is ...

  [tex]|3AB^5C^T|=3^3(-32) = \boxed{-864}[/tex]

Answer:

(a) The mean of the weight of the mice is 50.26 grams.

(b) The standard deviation of the weight of the mice is 14.08 grams.

Step-by-step explanation:

(a)

The mean is given as follows:

[tex]\bar X=\frac{\sum f_{i}x_{i}}{\sum f_{i}}[/tex]

    [tex]=\frac{5026}{100}\\\\=50.26[/tex]

Thus, the mean of the weight of the mice is 50.26 grams.

(b)

Compute the standard deviation as follows:

[tex]s=\frac{1}{\sum f_{i}-1}[\sum f_{i}x_{i}^{2}-\frac{1}{\sum f_{i}}(\sum f_{i}x_{i})^{2}][/tex]

  [tex]=\frac{1}{100-1}[254001-\frac{1}{100}(5026)^{2}]\\\\=\frac{1}{99}\times 1394.24\\\\=14.08323\\\\\approx 14.08[/tex]

Thus, the standard deviation of the weight of the mice is 14.08 grams.

x = number of 1-cent stamps

y = number of 8-cent stamps

z = number of 12-cent stamps

We have 31 stamps all together, so x+y+z = 31.

"I have 4 more 1-cent stamps than 8-cent stamps" means we have the equation x = y+8. Whatever y is, add 8 to it to get x. Solve for y to get y = x-8.

You also have "twice as many one cent stamps as 12 cent stamps", so x = 2z. Solving for z gets you z = 0.5x

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

x+y+z = 31

x+x-8+z = 31 ... y replaced with x-8

x+x-8+0.5x = 31 ... plug in z = 0.5x

2.5x-8 = 31

2.5x = 31+8

2.5x = 39

x = 39/2.5

x = 15.6

Your teacher made a typo somewhere because we should get a positive whole number result for x (since x is a count of how many 1-cent stamps we have).

The number of one-cent stamps is 14.

Total stamps = 31
We have three types of stamps: 1-cent stamps, 8-cent stamps, and 12-cent stamps.

The person has 4 more 1-cent stamps than 8-cent stamps.

The person has twice as many 1-cent stamps as 12-cent stamps.

We have to make equations with the given above statement.

Consider,

1-cent stamp = A

8-cent stamp = B

12-cent stamp = C

4 more 1-cent stamps than 8-cent stamps: A = 4 + B.

A = 4 + B

B = A - 4..........(1)

Twice as many 1-cent stamps as 12-cent stamps: A = 2C.

A = 2C

C = A/2...............(2)

Total number of stamps = 31

A + B + C = 31................(3)

Putting (1) and (2) in (3)

we get,

A + ( A - 4 ) + A / 2 = 31

A + A - 4 + A / 2 = 31

2A - 4 + A / 2 = 31

2A + A / 2 = 31 + 4

(4A + A) / 2 = 35

4A + A = 35 x 2

5A = 70

A = 70 / 5

A = 14

Thus the number of 1-cent stamps is 14.

Learn more about similar problems here:

https://brainly.com/question/16959755

#SPJ5

Answer:

7 pi cm^2 or  approximately 21.98 cm^2

Step-by-step explanation:

First find the area of the large circle

A = pi r^2

A = pi 3^2

A = 9 pi

Then find the area of the small unshaded circle

A = pi r^2

A = pi (1)^2

A = pi

There are two of these circles

pi+ pi = 2 pi

Subtract the unshaded circles from the large circle

9pi - 2 pi

7 pi

If we approximate pi as 3.14

7(3.14) =21.98 cm^2

Answer:

[tex]\boxed{\sf 7\pi \ cm^2 \ or \ 21.99 \ cm^2 }[/tex]

Step-by-step explanation:

[tex]\sf Find \ the \ area \ of \ the \ two \ smaller \ circles.[/tex]

[tex]\sf{Area \ of \ a \ circle:} \: \pi r^2[/tex]

[tex]\sf r=radius \ of \ circle[/tex]

[tex]\sf There \ are \ two \ circles, \ so \ multiply \ the \ value \ by \ 2.[/tex]

[tex](2) \pi (1)^2[/tex]

[tex]2\pi[/tex]

[tex]\sf Find \ the \ area \ of \ the \ larger \ circle.[/tex]

[tex]\sf{Area \ of \ a \ circle:} \: \pi r^2[/tex]

[tex]\sf r=radius \ of \ circle[/tex]

[tex]\pi (3)^2[/tex]

[tex]9\pi[/tex]

[tex]\sf Subtract \ the \ areas \ of \ the \ two \ circles \ from \ the \ area \ of \ the \ larger \ circle.[/tex]

[tex]9\pi -2\pi[/tex]

[tex]7\pi[/tex]

Answer:

196 in/cm/m²

Step-by-step explanation:

Given that the scale factor is a : b , then the area factor is a² : b² Here the scale factor is 1 : 7 , thus area scale factor is 1² : 7² = 1 : 49 That is the area of the dilated square is 49 times the original square. area of dilated square = 4 × 49 = 196 in/cm/m²

Answer:

yes

Step-by-step explanation:

every negative any positive number is an integer

Answer:

Step-by-step explanation:

No.  Integers do not have fractions in them.

-2.75 is equivalent to -275/100, which is a fraction that does not reduce to an integer

Answer:

Total interest = $3.41

Step-by-step explanation:

Since she can pay $72 each month we can divide the payments on monthly basis till all the money is paid.

The annual interest rate is 24.7%, so the monthly rate will be 24.7 ÷ 12= 2.058%

For the first month

With payment of $72 the remaining amount will be 189.56 - 72 = $117.56

Interest paid will be 0.02058 * 117.56 = $2.42

Total amount owed now will be 117.56 + 2.42 = $119.98

For the second month another payment of $72 is made

The remaining will be 119.98 - 72 = $47.98

Interest charged will be 0.02058 * 47.98 = $0.99

The amount owed will be 47.98 + 0.99 = $48.97

In the third month she will pay the remaining $47.98 which is within her monthly limit

Total interest paid = Sum of Amount paid each month - Initial amount spent

Total interest = {(72 * 2) +48.97} - 189.56 = $3.41

Answer:

33 Litres

Step-by-step explanation:

6 pounds of strawberries and 1 pound of blueberries

I did the quiz

9514 1404 393

Answer:

  10.7 years

Step-by-step explanation:

The formula for the balance in an account earning compound interest is ...

  A = P(1 +r/n)^(nt)

where principal P is invested at annual rate r compounded n times per year for t years. We want to solve for t.

  5800 = 3500(1 +0.0475/4)^(4t)

  58/35 = 1.011875^(4t) . . .  divide by 3500 and simplify a bit

  log(58/35) = 4t·log(1.011875) . . . . take logs

  t = log(58/35)/(4·log(1.011875)) . . . . divide by the coefficient of t

  t ≈ 10.6966 ≈ 10.7

The person must leave the money n the bank for about 10.7 years for it to reach $5800.

Answer:

Hello,

Answer 162

Step-by-step explanation:

Let say n the searched number.

[tex]n=\overline{abc}\\a>0\\c=a+1\\b=2*(a+c)\\\\.T.\ means\ True.\\\\\\\begin{array}{c|c|c|c}a&c&b&ok\\1&2&6&.T.\\3&4&14&.F.\\5&6&22&.F.\\7&8&30&.F.\end{array}\\\\\\\boxed{Answer\ n=162}\\[/tex]

Answer:

No image I cannot tell you

Step-by-step explanation:

Answer:

The probability of raining if the number of days is more than 23 is 0.0668.

Step-by-step explanation:

We are given that the mean number of days to observe rain in a particular city is 20 days with a standard deviation of 2 days.

Let X = Number of days of observing rain in a particular city.

The z-score probability distribution for the normal distribution is given by;

                         Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean number of days = 20 days

           [tex]\sigma[/tex] = standard deviation = 2 days

So, X ~ Normal([tex]\mu=20, \sigma^{2} = 2^{2}[/tex])

Now, the probability of raining if the number of days is more than 23 is given by = P(X > 23 days)

        P(X > 23 days) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{23-20}{2}[/tex] ) = P(Z > 1.50) = 1 - P(Z [tex]\leq[/tex] 1.50)

                                                              = 1 - 0.9332 = 0.0668

The above probability is calculated by looking at the value of x = 1.50 in the z table which has an area of 0.9332.

The answer is -13.8.

Hope this helps!

By the fundamental theorem of calculus,

[tex]E(t)=E(1)+\displaystyle\int_1^t E'(u)\,\mathrm du[/tex]

So we have

[tex]E(t)=92+\displaystyle\int_1^t(75-6u)\,\mathrm du[/tex]

[tex]E(t)=92+(75u-3u^2)\bigg|_1^t[/tex]

[tex]E(t)=20 + 75 t - 3 t^2[/tex]

Answer:

the domain is all real numbers

Answer:

0.0090483

Approximately = 0.00905

Step-by-step explanation:

z = (x - μ)/σ, where

x is the raw score = 3.74

μ is the sample mean = population mean = 4 mm

σ is the sample standard deviation

This is calculated as:

= Population standard deviation/√n

Where n = number of samples = 100

σ = 1.1/√100

σ = 1.1/10 = 0.11

z = (3.74 - 4) / 0.11

z = -2.36364

Using the z score table to determine the probability,

The probability that the average thickness of the 100 sheets is less than 3.74 mm

P(x<3.74) = 0.0090483

Approximately = 0.00905

Using the normal distribution and the central limit theorem, it is found that there is a 0.0091 = 0.91% probability that the average thickness of the 100 sheets is less than 3.74 mm.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

The probability is the p-value of Z when X = 3.74, then:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{3.74 - 4}{0.11}[/tex]

[tex]Z = -2.36[/tex]

[tex]Z = -2.36[/tex] has a p-value of 0.0091.

0.0091 = 0.91% probability that the average thickness of the 100 sheets is less than 3.74 mm.

A similar problem is given at https://brainly.com/question/14228383

This question is incomplete.

Complete Question

Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?

Answer:

280 tons of wood.

Step-by-step explanation:

From the above question:

To make 1 ship = we require 40 tons of wood.

1 ship = can accommodate 300 sailors.

Step 1

If :

300 sailors = 1 ship

2100 sailors = y ships

Cross Multiply

300 × y ships = 1 ship × 2100 sailors

y ships = 2100 / 300

y ships = 7

Hence, 2100 sailors can occupy 7 ships.

Step 2

We are told in the question that:

Astrid wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?

If:

1 ship = 40 tons of wood

Since 7 ships can accommodate 2100 sailors,

7 ships =

7 × 40 tons of wood = 280 tons of wood.

Therefore , Astrid needs 280 tons of wood to accommodate 2100 sailors.

Answer:

6x-3=21

6x=24

x=4

........

6x+27=39

6x=39-27

6x=12

x=2

........

8x-10=14

8x=24

x=3

.........

6+6x=22

6x=22-6

x=3

......

12x-2=28

12x=26

x=3

.....

8-4x=16

-4x=8

x=-2

.....

4x-24=3x-3

4x-3x=24-3

x=21

....

9x+6=6x+12

9x-6x=12-6

3x=6

x=2

Answer:

Step-by-step explanation:

1. 3(2x - 1) = 21

 = 6x - 3 = 21

 = 6x = 24

 = x = 24/6 = 4

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

2. 3(2x+9) = 39

   = 6x + 27 = 39

   = 6x = 39 - 27

   = 6x = 12

   = x = 12/6 = 2

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

3. 2(4x - 5) = 14

  = 8x - 10 = 14

  = 8x = 14+10

 = x = 3

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

9514 1404 393

Answer:

  C. symmetric with respect to the origin

Step-by-step explanation:

A graph must pass the vertical line test to be called the graph of a function. No function will ever be symmetrical with respect to the x-axis, because that would mean it fails the vertical line test.

An even function is symmetrical about the y-axis. An even function has the characteristic that ...

  f(-x) = f(x) . . . . an even function

An odd function is symmetrical about the origin. An odd function has the characteristic that ...

  f(-x) = -f(x)

__

The given function is f(x) = -1/x. Then the value of f(-x) is ...

  f(-x) = -1/-x = 1/x = -f(x)

The given function is an odd function, so is symmetrical about the origin.

Answer:

[tex] S_6 = -63 [/tex]

Step-by-step explanation:

The sequence above is a geometric sequence.

The common ratio (r) = [tex] \frac{-6}{3} = \frac{12}{-6} = -2 [/tex]

The common ratio < 1, therefore, the formula for the sum of nth terms of the sequence would be: [tex] S_n = \frac{a_1(1 - r^n)}{1 - r} [/tex]

a1 = 3

r = -2

n = 6

Plug in the values into the formula

[tex] S_6 = \frac{3(1 - (-2^6)}{1 - (-2)} [/tex]

[tex] S_6 = \frac{3(1 - (64)}{1 + 2} [/tex]

[tex] S_6 = \frac{3(-63)}{3} [/tex]

[tex] S_6 = -63 [/tex]