Derive linear equations iready

The equation is 25x + 8 = 183

The value of x is 7

The group of friends have $183 to spend

The cost of parking is $8

The tickets cost $25 per person

The equation can be written as follows

25x + 8 = 183

Collect the like terms

25x= 175

Divide by the coefficient of x which is 25

x= 175/25

x= 7

Hence the value of x is 7 and the equation is written as 25x + 8 = 183

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Answer:

the x-coordinate and y-coordinate change places.

Step-by-step explanation: so you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).

Answer:

slope=3

Step-by-step explanation:

The two numbers are 7/6 and 5 when the sum of two numbers is 3 more than four times the first number.

Let's call the two numbers x and y, where x is the first number and y is the second number.

The problem gives us two equations that relate the two numbers:

\(x + y = 3 + 4x\\y - x = 2y - 10\)

We can substitute the expression for y from equation 1 into equation 2:

\(y - x = 2(3 + 4x) - 10\)

Expanding the right side and simplifying, we get:

\(y - x = 6 + 8x - 10\\y - x = 8x - 4\)

Adding x to both sides:

\(y = 9x - 4\)

Substituting this expression for y into equation 1:

\(x + (9x - 4) = 3 + 4x\)

Expanding and simplifying the right side:

\(10x - 4 = 3 + 4x\)

Subtracting 4x from both sides:

\(6x - 4 = 3\)

Adding 4 to both sides:

\(6x = 7\)

Dividing both sides by 6:

\(x = 7/6\)

Substituting this value of x back into the expression for y:

\(y = 9x - 4 = 9 * (7/6) - 4 = 63/6 - 4 = 9 - 4 = 5\)

So the two numbers are 7/6 and 5.

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If shareholders in an electronics company were informed that the company's market share increased from 4.5% to 5.4%, a rise of 0.9 percentage points. The percent increase in sales that this represent is: 20%.

Using this formula

Percentage increase= Percentage increase in share price / Initial percentage x 100%

Let plug in the formula

Percentage increase= 0.9% / 4.5% x 100%

Percentage increase=20%

Therefore If shareholders in an electronics company were informed that the company's market share increased from 4.5% to 5.4%, a rise of 0.9 percentage points. The percent increase in sales that this represent is: 20%.

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Answer:

8:3

Step-by-step explanation:

You divide them both by 5.

Answer:

40:15 = 8:3

Step-by-step explanation:

This is the answer because:

1) Since there are 40 elephants and 15 baby elephants, the answer would be 40:15, but we want to simplify the ratio. In order to simplify the ratio, just divide each number by 5:

40 ÷ 5 = 8

15 ÷ 5 = 3

8:3

Therefore, the answer is 8:3.

Hope this helps! :D

Answer: a. 2(11a+14)

b. 47x-17

c. x^2+5x

d. x(x+8)

Step-by-step explanation:

a. 2a+4(7+5a)=

2a+4*7+4(5a)=

2a+28+20a=

22a+28=2(11a+14)

b. 4(3x+2)-5(7x+5)=

12x+8-35x-25=

12x+35x+8-25=47x-17

c. x(x+5)=x^2+5x

d. 2x+x(x+6)=

2x+x^2+6x=

x^2+8x=x(x+8)

The derivative of f(x) = x⋅5x is f'(x) = 10x, which means that the rate of change of the function at any point x is 10 times the value of x at that point.

Using the product rule of differentiation, we can find the derivative of the function f(x) = x⋅5x as follows:

f'(x) = (x)'(5x) + x(5x)'

where (x)' and (5x)' are the derivatives of x and 5x with respect to x, respectively.

(x)' = 1 (the derivative of x with respect to x is 1)

(5x)' = 5 (the derivative of 5x with respect to x is 5)

Substituting these values, we get:

f'(x) = 1⋅5x + x⋅5

Simplifying further, we get:

f'(x) = 5x + 5x

Therefore, f'(x) = 10x.

In conclusion, the derivative of f(x) = x⋅5x is f'(x) = 10x, which means that the rate of change of the function at any point x is 10 times the value of x at that point.

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The required coordinate vector of p(t) = -1 + 15t - 6t^2 relative to B is [2, -2, 3].

The basis for P2 as B = {1 - 4t2, 2 - t, 1 + t - t2}.We need to find the coordinate vector of p(t) = -1 + 15t - 6t2 relative to the basis B of P2.Coordinate vector relative to B means expressing p(t) as a linear combination of the basis vectors, and then finding the scalars (coefficients of the linear combination) and arranging them in a column vector.Consider the vector space P2 consisting of all polynomials of degree less than or equal to 2.Let p(t) be an arbitrary element of P2. Then we need to express p(t) as a linear combination of the given basis vectors, i.e.,p(t) = c1(1 - 4t^2) + c2(2 - t) + c3(1 + t - t^2)where c1, c2, and c3 are scalars. Equating the coefficients of the corresponding powers of t, we get-1 = c1 + 2c2 + c315 = -4c1 - c27 = c1 + c2 - c3Therefore, solving the above equations for c1, c2, and c3, we getc1 = 2, c2 = -2, and c3 = 3.Now, the coordinate vector [P]b of p(t) relative to B is given by[P]b = [2, -2, 3]Hence, the required coordinate vector of p(t) = -1 + 15t - 6t^2 relative to B is [2, -2, 3].Answer: [2, -2, 3].

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Answer:

The Watermelon candies cost 13 more cents then the chocolate.

Step-by-step explanation:

$3.48 divided by 12 is 29 cents

$1.28 divided by 8 is 16 cents

Subtract 16 from 29 and get 13

If Lickety Sweet's Candy Store sells candy by the ounce. Maura paid $3.48 for a 12-ounce bag of hard watermelon candies and $1.28 for an 8-ounce bag of chewy chocolate candies, then she paid 13 more cents for watermelon candies cost per ounce than the chocolate candies

Two or more expressions with an Equal sign is called as Equation.

Given,

Lickety Sweet's Candy Store sells candy by the ounce.

For 12-ounce bag of hard watermelon candies Maura paid $3.48

For 8-ounce bag of chewy chocolate candies Maura paid $1.28

Let us find cost of each watermelon candie

$3.48 divided by 12

3.48/12=29 cents

$1.28 divided by 8

1.28/8=16 cents

Subtract 16 from 29 and get 13

29-16=13

Hence 13 cents more do the watermelon candies cost per ounce than the chocolate candies

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The first term of the infinite geometric series is 625.Let's dive deeper into the explanation.

We are given that the sum of the infinite geometric series is \(\( \frac{15625}{24} \)\)and the common ratio is\(\( \frac{1}{25} \).\)The formula for the sum of an infinite geometric series is \(\( S = \frac{a}{1 - r} \)\), where \( a \) is the first term and \( r \) is the common ratio.
Substituting the given values into the formula, we have \(\( \frac{15625}{24} = \frac{a}{1 - \frac{1}{25}} \).\)To find the value of \( a \), we need to isolate it on one side of the equation.
To do this, we can simplify the denominator on the right-hand side.\(\( 1 - \frac{1}{25} = \frac{25}{25} - \frac{1}{25} = \frac{24}{25} \).\)
Now, we have \(\( \frac{15625}{24} = \frac{a}{\frac{24}{25}} \).\) To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the equation as \( \frac{15625}{24} \times\(\frac{25}{24} = a \).\)
Simplifying the right-hand side of the equation, we get \(\( \frac{625}{1} = a \).\)Therefore, the first term of the infinite geometric series is 625.
In conclusion, the first term of the given infinite geometric series is 625, which corresponds to option (a).



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Answer:

11 degrees Fahrenheit

Step-by-step explanation:

-2 + 13 = 11

Answer:

11°F

Step-by-step explanation:

False. A vertical line drawn through a normal distribution at z = 1.25 will not separate the distribution into two sections with a proportion of 0.1056 in the smaller section.

In a normal distribution, the area under the curve represents probabilities, and the total area under the curve is equal to 1. The proportion in any specific section of the distribution is represented by the area under the curve within that section. However, the exact proportion will depend on the specific value of z and the distribution's parameters.

When looking up a proportion in a standard normal distribution table, the table typically provides the area to the left of a given z-score. In this case, if we look up a z-score of 1.25 in the table, we find that the proportion to the left of z = 1.25 is approximately 0.8944. Therefore, the proportion in the smaller section (to the left of z = 1.25) would be 0.8944, not 0.1056. The proportion in the larger section (to the right of z = 1.25) would be 1 - 0.8944 = 0.1056.

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Answer:

4760

Step-by-step explanation:

Simple interest= principal× time ×rate/100

=3500×4×9/100

= 1260

Amount that will be in the bank after 4years= 3500+1260

=4760

Answer:

$2.42 For one Burger

$1.21 For one order of Fries

Step-by-step explanation:

4(2(x))+5x=15.73

Multiply the numbers: 4*2

8x+5x=15.73

Combine like terms: 8x+5x

13x=15.73

Divide both sides of the equation by the same term: 13

x=1.212307692307692

Round to the nearest hundredth

x=$1.21

A variable without a clear operational definition can greatly impact the accuracy and reliability of statistics performed on it. To ensure accurate and meaningful results, it is important to have clear, well-defined variables in any research study.

The lack of a clear definition can lead to inconsistencies in data collection, making it difficult to accurately interpret and analyze the results.

Step 1: When a variable has no clear operational definition, researchers may measure or interpret it in different ways, leading to inconsistencies in data collection.

Step 2: These inconsistencies can affect the reliability and validity of the collected data, which in turn impacts the accuracy of the statistical analysis performed.

Step 3: As a result, the findings from such analyses may not accurately represent the true relationships or patterns within the sample or the population, leading to incorrect conclusions.

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Answer:

I guess it would help you

The probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled is \(0.01667496\).

What is probability?

Probability is defined as the possibility of an event to occur.

An automated weight monitor can detect underfilled cans of beverages with probability \(0.98\)

Thus probability of success will be \(p=0.98\)

So probability of failure \(q=1-p=1-0.98=0.02\)

To find the first wrong detection happening on the tenth trial the first nine trials must be success followed by failure in the tenth trial.

Thus, required probability \(=p^9q^1=(0.98)^9(0.02)=0.01667496\)

Hence the probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled is \(0.01667496\).

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Answer:

61 tiles

Step-by-step explanation:

area = 14 x 11.5 = 61 ft²

each 1 foot square tile = 1 ft²

61/1 = 61 tiles

Answer:

XY = 13 cm

Step-by-step explanation:

Area of a triangle formula:

area = base × height / 2

a = bh / 2

Plug numbers into equation:

32.5 = b × 5 / 2

Multiply both sides by 2 to isolate the variable

65 = b × 5

Divide both sides by 5 to isolate the variable

13 = b

Check your work:

32.5 = 13 × 5 / 2

32.5 = 65 / 2

32.5 = 32.5

Correct

Answer:

13

Step-by-step explanation:

Area=½×b×h

32.5=½×b×5

32.5=5/2b

To get be multiply each side by reciprocal of 5/2 which is 2/5

b =13

Answer:

(x+22) + x = 88

Step-by-step explanation:

if x is how much your friend collected, then how much you collected would be x + 22 because you collected 22 more then her. and if you add both of those together to get how much you collected together (the total) you get 88. so x (your friends sea shells) plus x+22 (your sea shells) is 88. tell me if you also need help solving the actual equation

you have x+22 + x = 88

you combine like terms, in this case the Xs

and you get 2x + 22 = 88

then you subtract 22 to both sides because you want to get x alone

and you get 2x = 88 - 22

which is 2x = 66

then you divide by 2 on both sides

and you get x = 66/2

and you get x = 33

Answer:

40cm.

Step-by-step explanation:

40cm is the answer .

Answer:

312cm squared

Step-by-step explanation:

The area of one of the 4 small triangles is 30 cm squared, multiply this by 4 and you get 120cm squared. Then the area of the rectangle is 192cm squared, add these together and you get 312cm squared.

Answer:

1013

Step-by-step explanation:

(6)(7)(8−0)(3)+5

=42(8−0)(3)+5

=(42)(8)(3)+5

=(336)(3)+5

=1008+5

=1013

Answer:

She missed 6 questions.

Step-by-step explanation:

88% can be written as (88/100) or as 0.88.

You can set this as a ratio problem which is,  

88/100 = correct/50

correct = (88/100)*50       (multiply both sides by 50)

correct = 44

So, 50 (total questions) - 44 = 6 incorrect questions

The false statement about Sara and Ashley can be derived by examining the opportunity cost of producing a milkshake. Opportunity cost is the loss of other alternatives when one alternative is chosen.In an hour, Ashley can produce 10 milkshakes or 30 ice cream sundaes,

while Sara can produce 16 milkshakes or 80 ice cream sundaes. Since Sara can produce milkshakes more efficiently, she has a comparative advantage in producing milkshakes. So, the false statement is the first statement which is Ashley's opportunity cost of producing 1 milkshake is 3 sundaes.To maximize their total output of beef and corn, Charlie and Don should specialize in the product for which they have a comparative advantage.

They should allocate their resources to maximize the production of beef and corn by specializing in the product for which they have a comparative advantage. Therefore, Charlie produces beef and Don produces corn.The correct option is:O Sara's opportunity cost of producing 1 milkshake is 5 sundaes.O Charlie produces beef and Don produces corn.

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To draw a rectangular array for 24 x 18 on graph paper, we create a grid with 24 rows and 18 columns.

The partial-products algorithm for multiplying 24 and 18 involves breaking down the multiplication into smaller, manageable steps. The array helps visualize these steps and demonstrates why the algorithm yields the correct answer. Using the array, we start by dividing the 24 x 18 rectangle into smaller squares that represent individual partial products. Each row in the array corresponds to a digit in the multiplier (24), and each column corresponds to a digit in the multiplicand (18). We fill in the array by multiplying the corresponding digits in the multiplier and multiplicand.

For example, the first partial product is obtained by multiplying the rightmost digit of the multiplier (4) by each digit in the multiplicand (8, 1). We place the result, 32, in the corresponding square in the array. Similarly, we calculate the other partial products and place them in the corresponding squares. To find the final product, we sum up all the partial products in the array. In this case, we add up the values in all the squares to get 432, which is the correct answer to 24 x 18.

The array demonstrates why the partial-products algorithm works. By breaking down the multiplication into smaller steps and organizing them in the array, we ensure that each digit in the multiplier is multiplied by each digit in the multiplicand. The array visually represents the distributive property of multiplication, where each digit in one number is multiplied by each digit in the other number. Adding up the partial products gives the total product, ensuring the correct result. The array provides a visual proof of why the partial-products algorithm yields the correct answer to the multiplication problem.

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1) The amplitude c+ is c+l

2) The expectation value is 0

3) The uncertainty ΔSX is √(3/7) c+.

Now, we know that any wave function can be written as a linear combination of two spin states (up and down), which can be written as:

Ψ = c+ |+> + c- |->

where c+ and c- are complex constants, and |+> and |-> are the two orthogonal spin states such that Sx|+> = +1/2|+> and Sx|-> = -1/2|->.

Hence, we can write the given wave function as:Ψ = c+|+> + i/√7|->

Now, we know that the given wave function has been defined in Sx basis, and not in the basis of |+> and |->.

Therefore, we need to write |+> and |-> in terms of |l> and |r> (where |l> and |r> are two orthogonal spin states such that Sy|l> = i/2|l> and Sy|r> = -i/2|r>).

Now, |+> can be written as:|+> = 1/√2(|l> + |r>)

Similarly, |-> can be written as:|-> = 1/√2(|l> - |r>)

Therefore, the given wave function can be written as:Ψ = (c+/√2)(|l> + |r>) + i/(√7√2)(|l> - |r>)

Therefore, we can write:c+|l> + i/(√7)|r> = (c+/√2)|+> + i/(√7√2)|->

Comparing the coefficients of |+> and |-> on both sides of the above equation, we get:

c+/√2 = c+l/√2 + i/(√7√2)

Therefore, c+ = c+l

The amplitude c+ is a real number and is equal to c+l

The expectation value of the operator Sx is given by: = <Ψ|Sx|Ψ>

Now, Sx|l> = 1/2|r> and Sx|r> = -1/2|l>

Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= -i/√7(c+l*) + i/√7(c+l)= 2i/√7 Im(c+)

As c+ is a real number, Im(c+) = 0

Therefore, = 0

The uncertainty ΔSX in the state |Ψ> is given by:

ΔSX = √( - 2)

where = <Ψ|Sx2|Ψ>and2 = (<Ψ|Sx|Ψ>)2

Now, Sx2|l> = 1/4|l> and Sx2|r> = 1/4|r>

Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= 1/4(c+l* + c+l) + 1/4(c+l + c+l*) + i/(2√7)(c+l* - c+l) - i/(2√7)(c+l - c+l*)= = 1/4(c+l + c+l*)

Now,2 = (2i/√7)2= 4/7ΔSX = √( - 2)= √(1/4(c+l + c+l*) - 4/7)= √(3/14(c+l + c+l*))= √(3/14 * 2c+)= √(3/7) c+

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