barry wrote 6 different numbers, one on each side of 3 cards, and laid the cards on a table, as shown. the sums of the two numbers on each of the three cards are equal. the three numbers on the hidden sides are prime numbers. what is the average of the hidden prime numbers?

The system of equations 5x+2y=-7 and 10x+4y= -14 has unique solution which is (-7/5,0).

In general, a system of linear equations can have one of three possible outcomes:

One unique solution (as in this case)

No solution (if the equations are inconsistent)

Infinitely many solutions (if the equations are dependent)

To solve this system of equations, we can use the method of elimination or substitution. Let's use the method of elimination, which involves adding or subtracting the equations to eliminate one variable.

First, we need to choose a variable to eliminate. Looking at the coefficients of x and y, we see that we can eliminate y by multiplying the first equation by -2 and adding it to the second equation:

-10x - 4y = 14

5x + 2y = -7

-5x = 7

Now we can solve for x:

-5x = 7

x = -7/5

We can substitute this value of x into one of the equations to solve for y. Let's use the first equation:

5x + 2y = -7

5(-7/5) + 2y = -7

-7 + 2y = -7

2y = 0

y = 0

Therefore, the solution to the system of equations is (x,y) = (-7/5,0).

This is called a unique solution, meaning there is only one possible solution for the system of equations.

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Complete Question:

Solve

5x + 2y = -7

10x + 4y = -14

And find the number of solutions for the equation

Answer:

Step-by-step explanation:

22.9

a) The cash deposit (down payment) that Melitha paid is R1,200.

b) The total amount (sum of periodic payments) that Melitha paid over 3 years is R12,094.20.

c) The monthly installment Melitha made is R335.95.

d) The total amount that Melitha paid for the music system is R13,294.20, including the total installments and initial deposit.

The down payment is the initial cash deposit made for the purchase of an item on credit.

The down payment provides financial evidence of the transaction and testifies about the borrower's ability to undertake the credit arrangement.

a) Cash deposit = R1,200 (R12,000 x 10%)

N (# of periods) = 36 months

I/Y (Interest per year) = 7.5%

PV (Present Value) = R10,800 (R12,000 - R1,200)

FV (Future Value) = R0

Results:

Monthly Payment (PMT) = R335.95

Sum of all periodic payments = R12,094.20

Total Interest = R1,294.20

Total amount paid for the music system = R13,294.20 (R1,200 + R12,094.20)

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Answer:

The sum of all numbers between 1 and 100 that are divisible by 4 or 7 can be found by using the concept of multiples. First, let's find all the multiples of 4 between 1 and 100. These are 4, 8, 12, 16, ..., 96. To find the number of multiples of 4 between 1 and 100, we can divide 100 by 4 and round down to the nearest whole number. That gives us 25. So, we have 25 multiples of 4 between 1 and 100.

Next, let's find all the multiples of 7 between 1 and 100. These are 7, 14, 21, 28, ..., 98. To find the number of multiples of 7 between 1 and 100, we can divide 100 by 7 and round down to the nearest whole number. That gives us 14. So, we have 14 multiples of 7 between 1 and 100.

Now we need to add up all the multiples of 4 and 7, but we have to make sure not to count any number twice, since some numbers may be divisible by both 4 and 7. For example, 28 is divisible by both 4 and 7. To avoid double counting, we need to find the multiples of 4 * 7 = 28. These are 28, 56, 84. There are 3 multiples of 28 between 1 and 100. So, we subtract these 3 numbers from the sum of all multiples of 4 and 7.

Finally, the sum of all numbers between 1 and 100 that are divisible by 4 or 7 is:

(4 + 8 + 12 + ... + 96) + (7 + 14 + 21 + ... + 98) - (28 + 56 + 84)

= (4 * 25) + (7 * 14) - (28 * 3)

= 100 + 98 - 84

= 114

So, the sum of all numbers between 1 and 100 that are divisible by 4 or 7 is 114.

The true proportion of all American adults who would report having earned money by selling something online in the previous year lies between 0.178 and 0.221.

A confidence interval is computed from the sample data and provides a range of values within which the true population parameter is expected to lie. The confidence level is the probability that the confidence interval contains the population parameter.

Using this critical value, we can construct a 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year. To do this, we use the formula:

confidence interval = sample proportion ± z* (standard error)

The sample proportion is the number of adults who reported earning money by selling something online (914) divided by the total sample size (4579), which gives us a proportion of 0.1997.

The standard error is calculated as:

standard error = √ [(sample proportion)(1 - sample proportion) / sample size]

Substituting the values, we get:

standard error = √ [(0.1997)(1 - 0.1997) / 4579] = 0.009

Plugging in the values, we get:

confidence interval = 0.1997 ± 2.33(0.009)

This gives us a confidence interval of 0.178 to 0.221.

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We need  9 sophomore girls to make sex and class independent when a student is selected at random.

No. of freshman boys     (fb) = 4

No. of freshman girls      (fg) = 6

No. of sophomore boys (sb) = 6

Let, the no. of sophomore girls = sg

The total number of students in the class T = fb + fg + sb +sg

                                                                     T = 4+6+6+sg

                                                                     T = 16 + sg

The probability of selecting a girl is  P(G) = (fg + sg) / T

                                                                    = (6+sg)/(16+sg)

The probability of selecting a sophomore is  P(S) = (sb + sg)/T

                                                                                  = (6+sg)/(16+sg)

As the events are independent, the probability of selecting a sophomore girl is                       P(sg) = P(G)*P(S)

                       sg/(16+sg) = (6+sg)*(6+sg)/(16+sg)(16+sg)

                       sg(16+sg)  = (6+sg)(6+sg)

                       16sg + [tex]sg^{2}[/tex] = 36 + 6sg + 6sg + [tex]sg^{2}[/tex]

                                 4sg = 36

                                   sg = 9

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Answer:

A van can carry 18 students; a bus can carry 41 students.

Step-by-step explanation:

Let v = capacity of van.

Let b = capacity of bus.

School A:

3v + 12b = 546

School B:

13v + 6b = 480

Our system of equation is:

3v + 12b = 546

13v + 6b = 480

      3v + 12b = 546

+  -26v - 12b = -960

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

    -23v         = -414

v = 18

3v + 12b = 546

3(18) + 12b = 546

54 + 12b = 546

12b = 492

b = 41

Answer: A van can carry 18 students; a bus can carry 41 students.

Answer:

answer is A

Step-by-step explanation:

because area of a rectangle is L × B

or length × width

since the length is expanded by x

10.5 (12x)

Answer:

Option C

Step-by-step explanation:

The original length of the room = 12 feet

After expansion, the new length = [tex](12 + x)[/tex] feet

Width of the room = 10[tex]\frac{1}{2}[/tex] feet = 10.5 feet

Area of a rectangle = Length × Width

The shape of the living room is a rectangle.

∴Area of living room = [tex](12 + x)[/tex] feet × [tex](10.5)[/tex] feet  
                                     [tex]= 10.5(12 + x)[/tex] square feet

Expand the brackets or parenthesis by applying the Distributive Law:

                                  [tex]= (12)(10.5) + (10.5)(x)[/tex] square feet

                                  = [tex](125 + 10x)[/tex] square feet

∴Option C

Answer:

the equation: 251+D=468

the answer: 217 miles

Step-by-step explanation:

Samantha drove a total of 468 miles, and she drove 251 miles on the first day. D would represent the distance traveled on the second day. The added distance traveled on both days will equal the total amount driven.

So, our equation will be 251 + D = 468.

To solve the equation,  we can use the inverse operations method in order to isolate D(the variable) To do that, we have to subtract 251 from both sides(both sides so that the equation still has the same value).

D=468-251.

Now we can simplify the equation to:

D=217.

The answer is: 217 miles will be traveled on the second day.

Answer:

A

Step-by-step explanation:

Answer: the answer is A

Step-by-step explanation:

We can see here that with the information given, one can prove that this quadrilateral is a parallelogram. Thus, it is yes>

A polygon with four sides and four vertices (corners) is called a quadrilateral. Its internal angles add up to 360 degrees.

Squares, rectangles, parallelograms, trapezoids, and rhombuses are all examples of quadrilaterals.

We can see that looking at the quadrilateral, we can deduce that it is parallelogram. This is because the opposites sides are equal. Also, their opposite angles are equal.

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The percent increase of the population in the past 10 years is 12.5%.

Percent​ increase is simply the amount of increase from the initial value to the new value in terms of 100 parts of the initial value.

It is expressed as;

C = ((x₂ - x₁) / x₁)100%

Where x₁ is initial value and x₂ is new value

Given that;

Plug in the given values into the above equation and simplify.

C = ((x₂ - x₁) / x₁) × 100%

C = (( 9000 - 8000 ) / 8000) × 100%

C = ( 1000 / 8000) × 100%

C = 0.125 × 100%

C = 12.5%

Therefore, the percent increase is 12.5.

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As a rule of thumb, altitude corrections of less than 100 feet for determining the pressure at a given altitude should be corrected using the standard pressure-altitude correction tables.

These tables provide the correction factor for the difference between the actual and standard atmospheric pressure at a given altitude. The correction factor can then be applied to the standard pressure value to obtain the actual pressure value at that altitude. Note that the standard atmospheric pressure is defined as 29.92 inches of mercury (in Hg) at sea level. The pressure decreases with increasing altitude in the lower atmosphere. The pressure-altitude correction tables provide a convenient and accurate way of determining the atmospheric pressure at different altitudes.

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Answer:

y= 1/2x + 5/2

Step-by-step explanation:

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

For the polynomial "8d⁻² - 4d³" , the standard form is  "-4d³ + 8d⁻²"  , the degree is "3"  and the leading coefficient is  "-4" and the number of terms is "2"  .

The polynomial is ⇒ 8d⁻² - 4d³.

To write the polynomial in standard form, we first rearrange the terms by putting the terms with the highest degree first ;

So , the standard form is ⇒ -4d³ + 8d⁻²  ;

The degree of the polynomial is 3, because it is the highest power of the variable "d" in the polynomial "-4d³ + 8d⁻²" .

The leading coefficient of the polynomial is "-4" , because it is the coefficient of the term with the highest degree.

The polynomial has 2 terms, so it is a binomial.

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The given question is incomplete , the complete question is

Write the polynomial " 8d⁻² - 4d³ " in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms.

Answer:

4a + b - $1.40 = 2b

Step-by-step explanation:

Different style of problem here, so here's my guess

Let...

A = Tshirts

B = Sweaters

4a + b - $1.40 = 2b

4a + b indicates 4 shirts plus 1 sweater

The -$1.40 at the end indicates $1.40 less than

=2b indicates 2 sweaters

There were 198 sailors and the ratio of18 pirates, so 198 divided by 19 equals 10.4, meaning there were approximately 176 pirates.

Find the ratio of pirates to sailors

Ratio of pirates to sailors

= 18 : 19

Convert the ratio to a fraction

Ratio of pirates to sailors

= 18/19

Find the number of pirates

Number of pirates

= (18/19) × 198

Number of pirates = 176

The ratio of pirates to sailors is 18 to 19. This means that for every 19 sailors, there are 18 pirates. To figure out how many pirates there are when there are 198 sailors, we can use a proportion. First, set up the proportion with the ratio given. The ratio is 18:19, so the proportion is 18/19 = x/198. Then, cross multiply, 18 x 198 = 19x. Now, divide both sides by 19, and we get 18 x 198/19 = x. Then, solve for x by multiplying both sides by 19, and we get 18 x 198 = 19x. Finally, divide both sides by 198 to get x, and x =176. So, there were approximately 176 pirates.

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Answer: look at the image for the answer and the solution

Step-by-step explanation:

Answer: the home of it is 78 degrees

Step-by-step explanation:

as the angular bisector is shown then we can say that its right

The value of the equation [tex]\frac{x+1}{x(1+x.e^x)}dx[/tex] after taking the integral is  [tex]ln ( \frac{x.e^x}{x.e^x+1} ) + c[/tex].

What is meant by the integral of an equation?

Calculating areas, volumes, and their extensions require the use of integrals, which are the continuous equivalent of sums. One of calculus' two fundamental operations is integration, which involves computing integrals. The other essential operation is differentiation. The area under the graph of a function for some interval can be expressed numerically as the integral (definite integral), or a new function can be created whose derivative is the original function (indefinite integral).

Given equation [tex]\frac{x+1}{x(1+x.e^x)}dx[/tex]

Multiply and divide the equation by eˣ

The equation becomes [tex]\frac{e^x(x+1)}{e^xx(1+x.e^x)}dx[/tex]

Now substitute eˣx = a

Differentiating both sides

[eˣ + xeˣ]dx = da

eˣ[1+x]dx = da

Substituting the above in the equation

[tex]\frac{e^x(x+1)}{e^xx(1+x.e^x)}dx = \frac{da}{a(1+a)}[/tex]

Now add and subtract a in the numerator

[tex]\frac{1 da}{a(1+a)} = \frac{a-a+1}{a(1+a)} da = \frac{a+1-a}{a(1+a)} da = \frac{1}{a} da - \frac{1}{a+1} da[/tex]

Now taking integral

[tex]\int \frac{1}{a} da -\int \frac{1}{a+1} da = ln(a) - ln(a+1) + c = ln ( \frac{a}{a+1} ) + c[/tex]

Now substituting back the value of a = eˣx

Therefore the value of the equation after taking the integral is  [tex]ln ( \frac{x.e^x}{x.e^x+1} ) + c[/tex].

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Answer: no it does not

Step-by-step explanation: Because 1,007 squared is 1,014,049 and the sum of 911 squared is 829,921 and then 829 squared is 687,241 then add 829,921+687,241=1,517,162 when it should equal 1,014,049 which is the amount of 1,007 squared to make it a right triangle.

The solution is : no, it does not form a right triangle.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

given that,

A triangular shaped region has side lengths of 829 miles, 911 miles, and 1,007 miles.

now, we get,

Because 1,007 squared is 1,014,049

and the sum of 911 squared is 829,921

and then 829 squared is 687,241

then add 829,921+687,241=1,517,162

when it should equal 1,014,049

which is the amount of 1,007 squared to make it a right triangle.

as we know that,

in right triangle,

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a^2 + b^2 = c^2.

so, we get,

The solution is : no, it does not form a right triangle.

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The total number of numbers less than 2016 with a digit sum of 8 is 116 numbers.

The sum of the digits in the positive whole numbers is to be 8.

So the possibilities are obtained by means of permutation as follows:

Three 0's and an 8;  ⁴P₁ = 4

One 1 and one 7, ⁴P₂ = 12

One 2 and one 6; ⁴P₂ = 12

One 3 and one 5; ⁴P₂ = 12

Two 1's and a 6; (⁴P₃/2!) = 12

One 1, one 2, and one 5; ⁴P₃ = 24

Two 2's and a 4; (⁴P₃/2!) = 12

Two 3's and a 2; (⁴P₃/2!) = 12

Two 4's and a 0; (⁴P₃/2!) = 12

Three 1's and a 5; (⁴P₃/3!) = 4

Total = 116 numbers

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Answer:

f(-3)=4

Step-by-step explanation:

The answer is 4. To get f(-3), you must plug in -3 into the x.

Therefore, -4(-3)-8=f(-3).

Then you multiply -4 and -3. 12-8=f(-3)

Finally, you subtract 8 and get the answer:

f(-3)=4

A centigram is 100 times larger than miligram as evident through comparison of the two values.

We know that centi can be represented as 1/100 and milli will be represented as 1/1000. Now, the magnitudes representing each of these will be in relation to gram. So, further calculating the times with which centigram is larger than miligram.

For this, the expression to be used is -

Value = centigram/milligram

Keep the values in formula to find the comparison

Value = 1/100 ÷ 1/1000

Rewriting the expression

Value = 1000/100

Performing division on Right Hand Side of the equation

Value = 100

So, we see that centigram is 100 times larger than miligram.

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Answer:

1/9 buckets of fish

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

The dolphins are fed 1/3 of a bucket of fish and the sea otters are fed 1/3 as much as the dolphins.

That is 1/3 of 1/3 buckets:

Step-by-step explanation:

the first equation is already (without any transformation) expressing y in terms of x.

we can use that identity in the second equation :

-2x - 4(5x + 3) = 10

-2x - 20x - 12 = 10

-22x = 22

x = -22/22 = -1

and then we use the first equation to solve for y :

y = 5×-1 + 3 = -5 + 3 = -2

so,

x = -1

y = -2