If I do 100 Joules of work to lift my backpack, then half of everything falls out so that I can lift it using half the force, how much work will I do to lift it the same distance?

Stacy's age is 3 less than 4 times what her age was 6 years ago. The  algebraic equation to express this is x = 4(x - 6) - 3. A pair of pants was originally selling for $135, and discounted by 25% before an 9% tax was applied. The cost of the item after the discount and tax is $110.36.

1) Let's begin by defining a variable for Stacy's age. We'll use x to represent her current age.
According to the question, Stacy's age is 3 less than 4 times what her age was 6 years ago. We can write this as an algebraic equation:
x = 4(x - 6) - 3
Now, we'll solve for x by simplifying and isolating the variable on one side of the equation:
x = 4x - 24 - 3
x = 4x - 27
27 = 3x
x = 9
So, Stacy's current age is 9.

2) To find the cost of the item after the discount and tax, we'll first calculate the discount amount and then the tax amount.
The discount amount is 25% of the original price, so we'll multiply the original price by 0.25:
$135 * 0.25 = $33.75
Now, we'll subtract the discount amount from the original price to find the discounted price:
$135 - $33.75 = $101.25
Next, we'll calculate the tax amount by multiplying the discounted price by the tax rate of 9%:
$101.25 * 0.09 = $9.11
Finally, we'll add the tax amount to the discounted price to find the final cost of the item:
$101.25 + $9.11 = $110.36
So, the cost of the item after the discount and tax is $110.36.

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The scale factor from the map to the actual hiking trails can be found to be 50, 000.

To find the scale factor, we first need to look at the scale which is :

3 cm : 1. 5 km

This scale needs to have the same units of measurement so we can convert the  1.5 km to centimeters.

This becomes :

= 1. 5 x 100, 000 cm per km

= 150, 000 cm

The scale factor for the map to the actual hiking trails is :

= 150, 000  / 3

= 50, 000

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Answer:

The sum is 611105.

Answer:

782,886

Step-by-step explanation:

Statistically significant means that the relationship between two variables is likely to be real and not due to chance. If the p-value is lower than the predetermined threshold, usually 0.05, then the correlation is said to be statistically significant.

When a correlation between two variables is said to be statistically significant, it means that the relationship between the two variables is not due to chance or random error. In other words, the relationship is likely to be a real one and not just a coincidence.

Statistical significance is often determined by calculating a p-value, which is the probability of observing a relationship as strong as the one observed if there was no actual relationship between the variables. If the p-value is less than a predetermined threshold, usually 0.05, the relationship is considered to be statistically significant. This means that there is less than a 5% chance that the relationship observed is due to random error.

Therefore, It is usually determined by calculating a p-value, which measures the probability that the relationship between two variables is due to random chance.

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Answer:

  3-4-5 right triangle is scalene

Step-by-step explanation:

You want to show the triangle defined by points P(3,2),Q(6,2) and R(6,6) is a scalene triangle.

We observe that points P and Q have the same y-coordinate, so lie on the horizontal line y=2. The length PQ is 6 -3 = 3 units.

Points Q and R have the same x-coordinate, so lie on the vertical line x=6. The length QR is 6 -2 = 4 units.

These legs are different lengths and are at right angles to each other. The third leg, the hypotenuse, will be longer than either of them.

The triangle's sides are unequal, so the triangle is a scalene triangle.

We need to round up to the next full number because we are unable to equation have a fraction of a boat. The organization will thus require 157 boats to hold the entire 1,254 persons.

Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.

We may divide the total number of persons by the capacity of each boat to determine the number of boats required to hold a party of 1,254 individuals:

8 individuals per boat times 1,254 passengers is 156.75 boats.

We need to round up to the next full number because we are unable to have a fraction of a boat. The organization will thus require 157 boats to hold the entire 1,254 persons.

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The value of (f-g)(x)  is  x^(2)-6x-55.

Mathematical operations on a function involve the manipulation or transformation of the function, such as adding, subtracting, multiplying, dividing, and integrating the function. These operations can be done either to the function itself or to the domain or range of the function. This can be used to find the inverse of a function, calculate the area under the curve, or find the first or second derivative of a function.

To find (f-g)(x), we need to subtract the function g(x) from the function f(x).

(f-g)(x) = f(x) - g(x)

= (x^(2)-5x-50) - (x+5)

= x^(2)-5x-50 - x - 5

= x^(2)-6x-55

Therefore, (f-g)(x) = x^(2)-6x-55.

This is the final answer for the difference between the two functions f(x) and g(x).

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For the given arithmetic series, a_(1) = 27, d = 4, a_(n) = 783, n = 190, and n^(2) = 36100.

The given arithmetic series is 27, 31, 35,..., 783.

To find the first term, a_(1), we can simply look at the first term in the series. Therefore, a_(1) = 27.

To find the common difference, d, we can subtract the first term from the second term, or the second term from the third term. Therefore, d = 31 - 27 = 4.

To find the nth term, a_(n), we can use the formula a_(n) = a_(1) + (n - 1)d. We know that a_(1) = 27, d = 4, and a_(n) = 783, so we can plug these values into the formula and solve for n:

783 = 27 + (n - 1)(4)

756 = (n - 1)(4)

189 = n - 1

n = 190

Therefore, the nth term is 190.

To find the value of n^(2), we can simply square the value of n:

n^(2) = 190^(2) = 36100

Therefore, the value of n^(2) is 36100.

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Answer:

Without more information about the diagram, it is impossible to determine the term that describes GI. The terms median, angle bisector, perpendicular bisector, and altitude are all related to different types of lines and segments in triangles. Depending on the context and information given in the diagram, GI could be any of these.

Step-by-step explanation:

wag na pa delete nito na bweweset ako ang bob0 ng admin

The standard form for the quadratic equation written in vertex form y = 2(x - 2)² + 5 is y = 2x² - 8x + 13.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

To change the equation y = 2(x - 2)² + 5 from vertex form to standard form, we need to expand the squared term and simplify the expression.

Here are the steps -

Start with the vertex form: y = 2(x - 2)² + 5.

Expand the squared term using the formula (a - b)² = a² - 2ab + b².

In this case, a = x and b = 2, so we have -

y = 2(x - 2)(x - 2) + 5

y = 2(x² - 4x + 4) + 5

Multiply the coefficient 2 by each term inside the parentheses -

y = 2x² - 8x + 8 + 5

Combine the constant terms -

y = 2x² - 8x + 13

This is the standard form of the quadratic equation.

In standard form, the quadratic equation is written as y = ax² + bx + c, where a, b, and c are constants.

In this case, a = 2, b = -8, and c = 13.

Therefore, the standard form is y = 2x² - 8x + 13.

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Answer:

Let's start by defining some variables to represent the given information:

T0 = 48°F (the current temperature)

deltaT = -1.5°F/hour (the rate of change in temperature)

T = 36°F (the target temperature)

We want to find how many hours it will take for the temperature to drop from 48°F to 36°F, so let's call that time h. We can use the formula for the linear relationship between temperature and time:

T = T0 + deltaT * h

We want to solve for h when T = 36°F, so we can substitute the given values and solve for h:

36 = 48 + (-1.5) * h

-12 = -1.5h

h = 8

Therefore, it will take 8 hours for the temperature to drop from 48°F to 36°F, assuming the temperature continues to decrease at a rate of 1.5°F per hour.

There are 70 ways to assign 4 runners from a group of 8 to run the legs of the race.

Permutation and combination are two fundamental concepts in mathematics that deal with counting and arranging objects.

This is a combination problem. The formula for calculating the number of combinations of r items from a set of n items is:

nCr = n! / (r! * (n-r)!)

where n! represents the factorial of n, or the product of all positive integers up to and including n.

In this problem, we want to choose 4 runners from a group of 8, without regard to order. So we can use the combination formula as follows:

8C4 = 8! / (4! * (8-4)!)

= (8765) / (4321)

= 70

Therefore, there are 70 ways to assign 4 runners from a group of 8 to run the legs of the race.

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Answer:

400

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is 400 because you have to solve from left to right because of PEMDAS. So first you mutlipy 5x8 which is 40, and then you do 40x10 which is 400.

Answer:

3,200 kK

Step-by-step explanation:

Typically, only about 10% of the energy available at one trophic level is transferred to the next trophic level. This is known as the 10% rule, and it means that herbivores will only be able to incorporate about 10% of the energy available in the big bluestem grasses.

Therefore:

32,000 kJ x 0.10 = 3,200 kJ

The first 3 iterates of the function f(x) = 3x when x0=2 are,

⇒ 6, 18, 54

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The function is,

⇒ f (x) = 3x

At x₀ = 2

Now, We get;

The first iterate is,

⇒ f (x₁) = 3x₀ = 3 × 2 = 6

Second iterate is,

⇒ f (x₂) = 3x₁ = 3 x 6 = 18

Third iterate is,

⇒ f (x₃) = 3x₂ = 3 x 18 = 54

Thus, The first 3 iterates of the function f(x) = 3x when x0=2 are,

⇒ 6, 18, 54

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Kobe scored 656 points in the season.

How to find and what is basketball?

If Kobe scored 82 points in a basketball game and that was 1/8 of the points he scored for the season, we can find the total points he scored in the season by multiplying 82 by 8, since 82 represents 1/8 of the total points:

Total points = 82 x 8

= 656

Therefore, Kobe scored 656 points in the season.

Basketball is a team sport played between two teams of five players each. The objective of the game is to shoot a ball through a hoop or basket that is mounted on a backboard at each end of the court, while also preventing the opposing team from doing the same.

The game is played on a rectangular court with standardized dimensions and various markings, including a center circle, free-throw lines, and three-point lines. Basketball is a fast-paced and physically demanding sport that involves a combination of offensive and defensive skills, including shooting, dribbling, passing, and rebounding.

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The common ratio is equal to 3.

The tenth term of this geometric sequence is -78,732.

The explicit-formula of this geometric sequence is aₙ = -4(3)ⁿ⁻¹.

The three terms in the sequence after the last one given are -324, -972, and -2916.

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

Next, we would determine the common ratio as follows;

Common ratio, r = a₂/a₁

Common ratio, r = -12/-4

Common ratio, r = 3.

For the explicit formula, we have:

aₙ = a₁rⁿ⁻¹ = -4(3)ⁿ⁻¹

Now, we can determine three terms in the sequence after the last one given;

a₅ = a₁r⁵⁻¹ = -4(3)⁴ = -324.

a₆ = a₁r⁶⁻¹ = -4(3)⁵ = -972.

a₇ = a₁r⁷⁻¹ = -4(3)⁶ = -2916.

f(10) = a₁₀ = a₁r¹⁰⁻¹ = -4(3)⁹ = -78,732.

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The perimeter of the triangle PQR is 309 units

The figure represented in the question is a triangle

Given that the triangle side lengths are 92, 107 and 110

The total length of all sides of the triangle is equal to the perimeter of the triangle.

So, we have

Perimeter = 92 + 107 + 110

Evalyate the sum

Perimeter = 309

Hence, the perimeter is 309 units

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The proportion of observations in a standard Normal distribution that satisfies each of the given statements are:

1) P(z > -1.66) = 0.95154

2) P(-1.66 < z <2.85​) = 0.94936

Z table or z-score table is defined as a mathematical table that provides the values of cumulative density function for standard normal variates. It is used to determine the probability of a standard normal variate lying in a given interval.

We have to find the proportion of observations from a standard normal distribution that has a z-score between -1.66 and 2.85.

1) z > -1.66

From normal probability distribution table, we have that:

P(z > -1.66) = 0.95154

2) -1.66 < z <2.85​

From normal probability distribution table, we have that:

P(-1.66 < z <2.85​) = 0.94936

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Answer: 8 cubic inches

Step-by-step explanation:

Answer:

Volume of cube = length x width x height

V = 2x2x2

V = 8

Therefore, the volume of the box is 8 inches long.

For the system of linear equations

[tex]\[ \begin{aligned} h x_{1}-3 x_{2}-6 x_{3} & =-3 \\ x_{1}+3 x_{2}+x_{3} & =1 \\ -4 x_{1}-9 x_{2}+2 x_{3} & =-1 \end{aligned} \][/tex],  

the value of [tex]\( h \)[/tex] is [tex](15/4)x_2 + (30/4)x_3[/tex].

The value of h can be determined by using the elimination method to solve the system of equations.

First, multiply the second equation by 4 and the third equation by -1 to eliminate the x1 term: [tex]\[ \begin{aligned} 4 h x_{1}-12 x_{2}-24 x_{3} & =-12 \\ -4 x_{1}-12 x_{2}-4 x_{3} & =-4 \\ 4 x_{1}+9 x_{2}-2 x_{3} & =1 \end{aligned} \][/tex]

Next, add the second and third equations to the first equation: [tex]\[ \begin{aligned} 4 h x_{1}-15 x_{2}-30 x_{3} & =-15 \\ \end{aligned} \][/tex]

Now, divide the equation by 4 to solve for h: [tex]\[ \begin{aligned} h x_{1}-\frac{15}{4} x_{2}-\frac{30}{4} x_{3} & =-\frac{15}{4} \\ h x_{1}-\frac{15}{4} x_{2}-\frac{30}{4} x_{3}+\frac{15}{4} & =0 \\ h x_{1}-\frac{15}{4} x_{2}-\frac{30}{4} x_{3}+\frac{15}{4}-\frac{15}{4} & =-\frac{15}{4}+\frac{15}{4} \\ h x_{1}-\frac{15}{4} x_{2}-\frac{30}{4} x_{3} & =0 \\ h & =\frac{15}{4} x_{2}+\frac{30}{4} x_{3} \end{aligned} \][/tex]

Therefore, the value of h is dependent on the values of x2 and x3 and can be expressed as h = [tex](15/4)x_2 + (30/4)x_3[/tex].

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Answer:

Step-by-step explanation:

Answer is (A)

Replace [tex]6x-5y=1[/tex] with the sum of both equations in System A

Answer:

3/700

Step-by-step explanation:

hope this helps :))

a) The annual simple interest rate for this transaction is 16%.

b) Wolfgang paid $3,000 for the loan.

The annual simple interest rate is the percentage of the principal amount that is charged as interest for one year. It can be calculated using the formula I = P*R*T, where I is the interest, P is the principal amount, R is the annual interest rate, and T is the time in years.

(a) In this case, the principal amount is $2,500, the interest is $2,700 - $2,500 = $200, and the time is 180/360 = 0.5 years. We can plug these values into the formula and solve for R:

$200 = $2,500*R*0.5

$200 = $1,250*R

R = $200/$1,250

R = 0.16

The annual simple interest rate for this transaction is 16%.

(b) To find out how much Wolfgang paid for the loan, we can use the same formula and solve for P. The interest is $2,700 - $2,500 = $200, the annual interest rate is 20%, and the time is 120/360 = 0.3333 years:

$200 = P*0.20*0.3333

$200 = 0.06666*P

P = $200/0.06666

P = $3,000

Wolfgang paid $3,000 for the loan.

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B' is 11 right and 3 down from B.

A shape is translated when it is moved up, down, left, or right without turning. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.

Here, we have

Given: Point B​′​​(6,−5) is the image of B(−5,−2) under a translation.

The translation is from (-5, -2) to (6, -5). That is the values (h, k) was added to the coordinates where ...

-5 +h = 6

h = 11 . . . . . . . a translation of 11 to the right

and

-2 +k = -5

k = -3 . . . . . . . a translation of -3 upward is a translation of 3 downward.

Hence, B' is 11 units to the right and 3 units down from B.

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the solution is: population in 2015 will be 40,115,896

The exponential function is an illustration of a mathematical function that may be used to identify if something is increasing or decreasing exponentially. An exponential function employs exponents, as suggested by its name.

But, you should be aware that an exponential function does not have a constant base and a variable exponent (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

the median population change in California from 2000 to 2009 in percentage terms.

Given that there are 9 years, add up all the percentages, and then divide by 9.

1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93/9 = 1.3567%

From 2009 through 2015, there were six different time periods.

In the future, 37,000,000 x (1 + 0.013567) x 6 = 40,115,896.06

Hence, the solution is: population in 2015 will be 40,115,896

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The exponential function is y = 5*(∛2)^x and the value after 10 days is 50.4

Here we can see an exponential function of the form y = a*b^x

First, notice that it passes through (0, 5), then:

5 = a*b^0 = a

5 = a

So we got the initial value, so we can write the equaton like:

y = 5*b^x

And now we need to find the value of b.

We also can see that it passes through (3, 10), then:

10 = 5*b^3

10/5 = b^3

2 = b^3

∛2 = b

So the function is:

y = 5*(∛2)^x

b) The value after 10 days is what wet when we evaluate the function above in x = 10, then we will get:

y = 5*(∛2)^10  = 50.4

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Answer:

66y + 33

Step-by-step explanation:

Open up the parenthesis, then simplify

-11 (-2y - 3 - 4y)

22y + 33 + 44y

66y + 33

If you need it simplified, take 33 common

33 (2y + 1)

Answer:

66y+33

Step-by-step explanation:

22y+33+44y

66y+33

The sides of the triangle circumscribed about a circle of radius 4 and divided on one side by the circle into segments of length 6 and 8 are 6, 8, and 4.

The triangle circumscribed about a circle of radius 4 and divided on one side by the circle into segments of length 6 and 8 can be found using the Law of Cosines. The Law of Cosines states that c2 = a2 + b2 - 2ab cos C, where c is the length of the hypotenuse, a and b are the lengths of the other sides, and C is the angle opposite side c.

We know the hypotenuse of this triangle is 8, as it is the length of one of the segments on the side of the triangle. We also know that angle C is 90° as it is a right triangle.

Therefore, using the Law of Cosines we can find the length of the other side of the triangle, which is 6. The equation is 82 = 62 + a2 - 2(6)(a)cos(90°). Solving this equation, we find that a = 4.

Therefore, the sides of the triangle circumscribed about a circle of radius 4 and divided on one side by the circle into segments of length 6 and 8 are 6, 8, and 4.

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Laura's net proceeds were -$94.43. This means that she lost $94.43 on the transaction.

What is the commission?

A commission is a fee or percentage of a sale that is paid to a person or organization for their services in facilitating or completing a transaction. Commissions are commonly used in sales or business settings, where an individual or organization acts as a middleman between a buyer and a seller.

Laura's total cost for buying the stock was:

55 shares x $3.50/share = $192.50

Her broker's commission was 1% of $192.50, which is:

$192.50 x 0.01 = $1.93

So, her total cost including commission was:

$192.50 + $1.93 = $194.43

Her total revenue from selling the stock was:

55 shares x $2/share = $110

Her broker's fee for selling the stock was $10.

So, her total cost for selling the stock was:

$10

Therefore, Laura's net proceeds were:

$110 - $194.43 - $10 = -$94.43

This means that Laura lost money on the transaction.

Hence, Laura's net proceeds were -$94.43. This means that she lost $94.43 on the transaction.

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