Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25. This system of equations represents the situation, where x is the cost per pound of apples, and y is the cost per pound of bananas.

5x + 3y = 8.5

3x + 2y = 5.25

If you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate the y terms when making a linear combination?

Complete the multiplication and add the equations. What is the result?

What is the price per pound of apples? $

What is the price per pound of bananas? $

The Probability of P(F/E) is 0.5  .

Baye's Theorem helps in finding the conditional probability probability of an event A given that event B has already occurred.

For Example : The probability of event A given that event B has already occurred is denoted by P(A/B) and is calculated by

[tex]P(A/B)=\frac{P(A.and.B) }{P(B)}[/tex]

It is given in the question that

P(E and F)=0.1      and  

P(E)=0.2

Using Baye's Theorem ,we get

[tex]P(F/E)=\frac{P(F .and .E)}{P(E)}[/tex]

Substituting the values ,we get

[tex]P(F/E)=\frac{0.1}{0.2}\\ \\ =\frac{1}{2} \\ \\ =0.5[/tex]

Therefore , the probability of P(F/E) is 0.5  .

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The required value of y also gets divided by 7.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of y

let k be the constant of proportion

When a quantity varies directly with other quantity, then we have a relation, y = kx      

Now, find k for, some fixed value of x and y

Further, calculate y when x is divided by 7. In a general case, y will also be divided by 7 as both x and y varies directly.

Hence, the value of y also gets divided by 7.

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The answer in ascending order is -8/5, -0.7, 1.⁻3, [tex]\pi[/tex], [tex]\sqrt{13}[/tex]

What is ascending order?

Ascending order refers to the arrangement of numbers in ascending order, from least to greatest. We must first compare numbers before we may arrange them in any order. Count how many digits are in each number. The number with the fewest digits is the smallest.

The numbers arranged in ascending order are

-8/5, -0.7, 1.⁻3, [tex]\pi[/tex], [tex]\sqrt{13}[/tex]

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Answer:

Step-by-step explanation:

False inequality, so no solutions.

A quadrilateral has a perimeter of 12 and all of the side lengths are odd integer then the probability that the quadrilateral is a rhombus is 1/4.

If the midpoints of a rhombus with 12-inch sides are connected, a quadrilateral is created. A square with a 12-inch diagonal would be the quadrilateral that is constructed.

A perimeter is a closed path that encloses, surrounds, or delimits a one-dimensional length, a two-dimensional shape, or both. The circumference of a circle or an ellipse is its perimeter. There are numerous practical uses for calculating the perimeter.

All four side lengths must be added up in order to determine the perimeter, or the distance around the rectangle. Since there are two of each side length, it is simple to multiply the total of the length and the breadth by two in order to accomplish this task efficiently.

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Answer: i believe your answer is 21x=100

Step-by-step explanation: hope this helps

The correct expression and value is A. 9(n+8)-6, when n=5, the value is 111.

Firstly forming the expression using given information, starting the end of sentence. Breaking sentence into parts as follows -

1. the sum of a number and eight

2.  nine times the sum of a number and eight

3. six less than nine times the sum of a number and eight

Let the number be n.

So, equation according to 1. Sum = (n + 8)

Equation according to 2. 9(n + 8)

Equation according to 3. 9(n + 8) - 6

So, the expression is 9(n + 8) - 6

Now, keeping the value of n as 5 and finding the value of expression.

Value = 9(5 + 8 ) - 6

Firstly solving the bracket

Value = 9 × 13 - 6

Performing multiplication

Value = 117 - 6

Performing subtraction

Value = 111

Hence, the expression and value is A. 9(n+8)-6, when n=5, the value is 111

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The complete question is -

What is the expression and value of “six less than nine times the sum of a number and eight” when n = 5

A.9(n+8)-6, when n=5, the value is 111

B. 6-9(n+8), when n = 5, the value is 111

C. 9(n)+8-6, when n = 5 the value is 47

D.6-9(n), when n = 5, the value is 47

Answer:

The correct expression and value is A. 9(n+8)-6, when n=5, the value is 111.

Step-by-step explanation:

Answer:

50 pounds of raspberries and 45 pounds of apples is sold

Solution:

Let  "a" be the number of pounds of raspberries sold

Let "b" be the number of pounds of apples sold

Cost of each pound of raspberry = $ 4

Cost of each pound of apple = $ 1.50

Austin made $267.50 from selling a total of 95 pounds of raspberries and apples

Therefore,

a + b = 95

b = 95 - a ------ eqn 1

Austin made $267.50. Therefore,

number of pounds of raspberries sold x Cost of each pound of raspberry + number of pounds of apples sold x Cost of each pound of apple = 267.50

4a + 1.50b = 267.50 --------- eqn 2

Substitute eqn 2 in eqn 1

4a + 1.5(95 - a) = 267.50

4a + 142.5 - 1.5a = 267.50

2.5a = 125

a = 50

Substitute a = 50 in eqn 1

b = 95 - 50

b = 45

Thus 50 pounds of raspberries and 45 pounds of apples is sold

Step-by-step explanation:

hope it helps u

Answer:

yes I need help

Step-by-step explanation:

I don't understand it very well.

Answer:

r = (n - p)/c

Step-by-step explanation:

n = p + cr

Subtract p from both sides

n - p = p + cr - p

n - p = cr

Divide both sides by c.

(n - p)/c = cr/c

r = (n - p)/c

The correct names for the given angle is ∠PHV.

How to name the any angle?

For naming any angle, the common vertex must come in the middle of the name.

But it could start with any of the end point.

Thus, the angle given can be named either ∠PHV or  ∠VHP.

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Answer:

So the number is -48

Step-by-step explanation:

Lets say that the number is x

(x /6)+12=4

       x/6=-8

          x=-48

Using quadratic equation, The equation for given value of zeros is equation is x² - 6x - 16 = 0.

f(x) = ax2 + bx + c, where a, b, and c are integers and an is not equal to zero, is a quadratic function.

A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they always have the same fundamental "U" form. The three graphs in the image below are all parabolas.

The following must be true if those are the 0s:

-2 + 2 = 0

8 - 8 = 0

We would thus get the following equation if we were to include them in a quadratic-based one:

(x + 2)(x - 8) = 0

x² - 8x + 2x - 16 = 0

FOIL

Roughly speaking, x² - 6x - 16 = 0

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Answer:

f(x) = x2 − 6x − 16

Step-by-step explanation:

Write the zeros as solutions of two equations.

x  =  −2  x  =  8  

x + 2  =  0   x − 8  =  0  Rewrite each equation so that it equals 0.

Find the product of the two binomials.

(x + 2)(x − 8)  =  x2 − 8x + 2x − 16   Multiply.

=  x2 − 6x − 16  Simplify.

Rewrite the equation in function notation.

f(x) = x2 − 6x − 16

Therefore, the quadratic function with zeros of −2 and 8 is f(x) = x2 − 6x − 16.

The sum of the first 10 terms of the arithmetic series x+(x+y)+(x+2 y)+ . . . . . is S(10) = 10x+45y

The given arithmetic series:

     x+(x+y)+(x+2 y)+ . . . . .

Notice that:

a(1) = x

a(2) = x+y

a(3) = x+2y

We can find the common difference:

d = a(2) - a(1)

  = (x+y) - x = y

Recall the formula for the nth term of an arithmetic series:

a(n) = a(1) + (n - 1) . d

Substitute n = 10, a(1) = x, and d = y into the formula:

a(10) = x + (10 - 1)y

a(10) = x+9y

Use the sum formula:

S(n) = n/2 [a(1) + a(n)]

S(10) = 10/2 [x + (x+9y)]

S(10) = 5 .(2x+9y)

S(10) = 10x+45y

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if f(x)=2x+2

and f(x)= -1

2(-1) +2

-2 + 2 =0

the value would be 0

Answer:

X = 2

Step-by-step explanation:

4x-2 = 2x+2 multiply the brackets on both sides

4x-2x = 2+2 bring thes x's to one side & the constants to another side

2x = 4 simplify

X = 4÷2 divide

x = 2

2.25 kilometers on the ground is represented by 9cm on the map

According to the question, the scale on the map is in the ratio 1 : 25000

That is the     length on the map = length of the ground

                               1cm = 25000 cm

                                1 cm = 25000/100000 km

                                1 cm = 0.25 km

Now we have to find the length of the ground in kilometres which is represented by 9cm on the map

That is we have to find the ratio,  9cm : x km

As from above, we know that,

                          1cm = 0.25 km

                           9 cm = 0.25*9 km

                                    = 2.25 km

Hence 2.25 km on the ground is represented by 9 cm on the map

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Answer:

[tex]84n-27[/tex]

Step-by-step explanation:

[tex]-9(1-10n) -2(3n+9)[/tex]

[tex]-9+90n-6n-18[/tex]

[tex]{84n-27}[/tex]

Answer:

Jajajjajjajj

Step-by-step explanation:

The missing terms of the given arithmetic sequence AP are 14, 21, 28, 35.

An arithmetic progression (AP) is a sequence with the same distinctions between each successive term.

Now, in response to the question;

The arithmetic sequence.14,..., 28, ............

There are total 4 terms in the series.

Let the initial term is  'a₁' is given as 14.

Let the second term is 'a₂'.

Let the third term be 'a₃' which is given as 28.

Ans, the let the fourth term is represented as 'a₄'.

As, we know that in the AP, the difference of the two consecutive terms is equal and called as common difference.

Thus,

d = a₂ - a₁      ........(equation 1)

d = a₃ - a₂     .......(equation 2)

Thus, equating the two equation;

a₂ - a₁ = a₃ - a₂

Substituting the values;

a₂ - 14 = 28 - a₂

Simplifying the equation;

2a₂ = 28 + 14

2a₂ = 42

a₂ = 21.

Put the obtained value in equation 1 and find d.

d = a₂ - a₁

d = 21 - 14

d = 7

Now, estimate a₄.

a₄ = a₃ + d

a₄ = 28 + 7

a₄ = 35

Therefore, the complete arithmetic sequence is 14, 21, 28, 35.

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y=mx+c, where m is slope. Here x=-2, x-intercept at (x,y)=(-2,0)

and there is no y intercept.

y=mx+c, where m is slope.

The x-intercept is the value of x when y=0.

Since x=-2 for all values of y

it follows that x=-2 when y=0.

The y-intercept is the value of y when x=0 (or alternately the solution point of the form 90,y)). since x neq 0 not matter what value is assigned to y, no such point exists (graphically x=-2 is a vertical line parallel to, and therefore never intersecting, the Y-axis).

Therefore  x-intercept at (x,y) is (-2,0) and there is no y intercept.

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The geometric mean between the pair of numbers, 18 and 1.5, is 3√3.

Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.

To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.

The formula for the geometric mean is given by:

GM = n√x1 x2 . . . xn

Solving for the geometric mean between 18 and 1.5 using the formula:

GM = n√x1 x2 . . . xn

where n = 2, x1 = 18, and x2 = 1.5

GM = √(18)(1.5)

GM = √27

GM = 3√3

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By applying the exponent rule of division, the equivalent expression to  [tex]r^m \div r^n[/tex] is: A. [tex]r^{m - n}[/tex].

Given the expression, [tex]r^m \div r^n[/tex], we can find the expression that is equivalent to it by rewriting the expression as shown below:

r^m ÷ r^n

According to the exponent rule of division, if we are to divide two bases together that have the same same base but different exponents, what we only need to do is to subtract their powers.

We would apply this same rule in this given problem.

Applying the exponents rule of division, we would subtract the powers:

r^m ÷ r^n = r^(m - n)

Therefore, by applying the exponent rule of division, the equivalent expression to  [tex]r^m \div r^n[/tex] is: A. [tex]r^{m - n}[/tex].

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Answer:

It's a single number used to describe a set of numeric data.

The true statements are

The original statement is given as:

If a number is negative, the additive inverse is positive

This can be represented as

If p, then q

i.e. if p → q

So, (a) is correct

For the inverse, we simply negate the hypothesis and the conclusion

i.e. if ¬p → ¬q ----(b) is correct

For the converse, we simply switch the hypothesis and the conclusion

i.e. if q → p ----(e) is correct

Hence, the true statements are (a), (b) and (e)

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[tex]log_{5} \sqrt{14}[/tex] ≈ 0.82

The property of logarithms log ab = log a + log b , log a/b = log a - log b

[tex]log_{5} 2[/tex] ≈ 0.43

[tex]log_{5} 7[/tex] ≈ 1.21

We need to find,

[tex]log_{5} \sqrt{14}[/tex]

= 1/2[tex]log_{5} 14[/tex]

= 1/2[tex]log_{5} 2*7[/tex]     ( log ab = log a + log b)

= 1/2 ([tex]log_{5} 2[/tex] + [tex]log_{5} 7[/tex])  

=1/2( 0.43 + 1.21)

= 1/2 × 1.64

= 0.82

Hence logarithms of [tex]log_{5} \sqrt{14}[/tex] = 0.82

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An equation that relates T to N can be written as T = 750 + 560N.

An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.

A function can be defined as a mathematical expression which can be used to define and represent the relationship that exist between two or more variables in a population (data set).

Since the total amount saved by using both plans (functions A and B) is represented by T, an equation that relates T to N can be written as follows:

T = A + B

Substituting the given parameters into the formula, we have;

T = (750 + 165N) + 395N

T = 750 + 165N + 395N

T = 750 + 560N.

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Complete Question:

Ann and her husband are each starting a saving plan. Ann will initially set aside $750 and then add $165 every month to the savings. The amount A (in dollars) saved this way is given by the function A=750+165N , where N is the number of months he has been saving. Her husband will not set an initial amount aside but will add $395 to the savings every month. The amount B (in dollars) saved using this plan is given by the function B=395N. Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N.

Simplify your answer as much as possible.

The radius of a cylinder having height of 5cm and volume 770 cm³ is 7 cm.

Volume of a cylinder is the space occupied by it in a three - dimensional space.

Volume of a cylinder is calculated using the formula:

[tex]V = \pi r^{2} h[/tex]

[tex]r = \sqrt{\frac{V}{\pi h} }[/tex]

where r is the radius of the base of the cylinder.

is a constant having value 3.14

h is the height of the cylinder. It is the perpendicular height from the base.

According to the given condition,

V = 770 cm³ and h = 5 cm.

Substituting these values in the equation above,

∴ r = 7 cm

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