Manny took home a couple of his friends after soccer practice. He originally had 6 gallons of gas in his car. He used 1.04 gallons of gas to take one friend home and two fifths gallons to take the other friend home. How much gas did he have left in his car after taking both friends home?

You need to buy 80 cubic feet of sand to fill the sandbox.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The sandbox is a rectangular prism.

Length is 10 feet.

Width is 8 feet

Height is 1 feet.

Volume of prism=Length×Width×Height

=10×8×1

=80 cubic feet.

Hence, you need to buy 80 cubic feet of sand to fill the sandbox.

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The complete question is given in the attachment.

Answer: 7000 (4 s.f)

Step-by-step explanation:

[tex]x[/tex] x [tex]1.06^{11} = 13,288.09[/tex]

[tex]x = \frac{13,288.09}{1.06^{11} }[/tex]

[tex]x = 7000[/tex] (4 s.f)

This is a question where you make the equation by yourself using compound interest. If you have any further questions, feel free to ask me :)

the lunch cost, including tax and tip 67.31$.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, the Patterson family went to eat lunch at a new restaurant. They spent $52.30 on their meal. The restaurant will add a 7 1/4% tax to the cost of the meal.

total cost after the tax = 52.30*(1 + 7 1/4)%

total cost after the tax = 52.30* 7.25/100 + 52.30

total cost after the tax = 3.79 + 52.30

total cost after the tax = 56.09

Since,

Mr Patterson was very happy with the food and service so he gave a 20% tip to the waitress.

Thus,

Total cost after the tip = 56.09(1 +20/100)

Total cost after the tip = 56.09 * 1.2

Total cost after the tip =  67.308

Therefore, the lunch cost, including tax and tip 67.31$.

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The cost of one rose bush is $2 and the cost of one bunch of grass is $17.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, Norachai and Rain each improved their yards by planting rose bushes and grass.

Let the cost of rose bushes be x and the cost of bunches of grass be y.

Norachai spent $209 on 11 rose bushes and 11 bunches of grass.

Now, 11x+11y=209

x+y=19 --------(i)

Rain spent $40 on 3 rose bushes and 2 bunches of grass.

3x+2y=40 --------(ii)

Substitute x=19-y in equation (ii), we get

3(19-y)+2y=40

57-3y+2y=40

57-40=y

y=17

Substitute y=17 in equation (i), we get

x=2

Therefore, the cost of one rose bush is $2 and the cost of one bunch of grass is $17.

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Based on the information provided, it can be concluded the sum is $11,000.

To know what is the sum, let's calculate the difference in the interest rate:

13% - 12% = 1%

This means the difference between the two interest rates presented is 1%. Based on this, let's calculate the 1% of the sums given:

Based on the above, the correct sum is $11,000 because only in this one 1%  is equivalent to $110.

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The locus of point P is a circle with center at the midpoint of points M and N, and radius equal to half the distance between the two points.

The midpoint of M and N is given by:

((-4+1)/2, (3+0)/2) = (-1.5, 1.5)

The distance between M and N is given by the distance formula:

√((1-(-4))^2 + (0-3)^2) = sqrt(25 + 9) = √(34)

So, the radius of the circle is √(34)/2.

Hence, the equation of the locus of point P is given by:

(x-(-1.5))^2 + (y-1.5)^2 = (√(34)/2)^2

or

(x+1.5)^2 + (y-1.5)^2 = (√(34)/2)^2

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Answer:

identical

Step-by-step explanation:

23 * 100 = 2.3 * 1000

they are the same

The constant of proportionality is, 12

Yes, The graph of equation is a straight line.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Mark is planning a birthday party at the local skating rink.

And, The table shows the rates that are charged for parties at the skating rink.

Let two points on table are (5, 60) and (10, 120)

Now, The equation of line is,

⇒ y - 60 = (120 - 60) / (10 - 5) (x - 5)

⇒ y - 60 = 60/5 (x - 5)

⇒ y - 60 = 12(x - 5)

⇒ y - 60 = 12x - 60

⇒ y = 12x

Thus, The number of guests proportional to the cost.

And, Constant of proportionality = 12

And, The graph of y = 12x is a straight line.

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Complete question is shown in figure.

The final solution to the given simultaneous equation is (0, -6)

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

Given the set of equations below:

y = -x-6

x + 3y = -18

Using the substitution method;

Substitute equation 1 into 2 to have:

x + 3(-x - 6) = -18
x - 3x - 18  =-18
-2x = 0

x = 0

Since y = -x- 6

y = -0 - 6

y = -6

Hence the solution to the system of equation is (0, -6)

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Answer:

[tex]\frac{43}{15}[/tex]x + 30

Step-by-step explanation:

3[tex]\frac{2}{3}[/tex]x - [tex]\frac{4}{5}[/tex] (x - 3[tex]\frac{3}{4}[/tex])

[tex]\frac{11}{3}[/tex]x - [tex]\frac{4}{5}[/tex] (x - [tex]\frac{15}{4}[/tex])

[tex]\frac{11}{3}[/tex]x - [tex]\frac{4}{5}[/tex] x + [tex]\frac{60}{20}[/tex]

[tex]\frac{11}{3}[/tex]x - [tex]\frac{4}{5}[/tex] x + 30

[tex]\frac{55}{15}[/tex]x - [tex]\frac{12}{15}[/tex] x + 30

[tex]\frac{43}{15}[/tex]x + 30

Answer:

P(≥ 4) = 0.44

Step-by-step explanation:

The experimental probability of landing on a number greater than or equal to 4 can be calculated by adding the frequency of outcomes 4, 5, and 6 and dividing by the total number of trials.

The frequency of outcomes 4, 5, and 6 is 6 + 9 + 7 = 22.

The experimental probability of landing on a number greater than or equal to 4 is 22/50 = 0.44.

So, the answer is B. P(≥ 4) = 0.44.

Answer:

P(≥ 4) = 0.44  

Step-by-step explanation:

I took the test and it was right!

The main difference between these exponential properties is that for (a^n)^m=a^(nm) we have the same base, hence we just just multiply the powers, applying the power of power rule. For a^nb^n=(ab)^n, we have different bases, hence the exponent is just a common factor.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

It can be applied if the bases are the same, that is:

(a^n)^m = a^(n x m) = a^(nm).

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If the variance of a distribution is 13.53, the value of its standard deviation is, 3.68.

And, If the standard deviation of a distribution is 3.45, the value of variance is, 11.90

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The variance of a distribution is 13.53,

And, The standard deviation of a distribution is 3.45.

We know that;

⇒ Standard deviation = √ Variance

Now, If the variance of a distribution is 13.53,

The value of its standard deviation is,

⇒ Standard deviation = √ Variance

⇒ Standard deviation = √13.53

⇒ Standard deviation = 3.68

And, If the standard deviation of a distribution is 3.45.

The value of variance is,

⇒ Standard deviation = √ Variance

⇒ 3.45 = √ Variance

⇒ Variance = 3.45²

⇒ Variance = 11.90

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Answer:

2 or -1

Step-by-step explanation:

[tex]1. \: y + 1 = 2x \\ 2. \: \frac{y + 1}{2} = x \\ 3. \: x = \frac{y + 1}{2} [/tex]

[tex]1. \: y = 2 \times 0 - 1 \\ 2. \: y = - 1[/tex]

Note that where the figure below contains two semi-circles that are tangent to each Other at point B and ray DE is tangent to both semicircles at points E and F, it is correct to state that ED = 6√2 (Option A).

A semicircle is a one-dimensional point collection that forms half of a circle in mathematics. It is a circular arc with a circumference of 180°. It just has one symmetry line.

Solving the ED, we have:

ΔDEM ~ ΔDFP

This means that MD/PD = EM/FP

MD/(MD + 9) = 3/6
6MD = 3MD + 27 (Collect like terms over the equation)
3MD = 27
MD = 9 (If both sides are divided by 9)

Note that

ED = √[MD²-EM²]
ED  = √9²-3²]
ED = 6√2

Thus, it is correct to state that ED =  6√2

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The correct option is the third one. The statement "The [tex]\lim_{x \to \0} f(x)=4[/tex] because both the left hand and the right hand limit is equal to 4" identifies and explains the function of limit.

The limit function in mathematics is a way of finding the value that a function or sequence approaches as the input values approach a certain point. It is used to determine the behavior of a function as the input values approach a certain point or their maximum or minimum values.

Where the above two limits say that when we approach zero from the negative side (the first one) and from the positive side (the second one), we must get the same value.

Remember that the limit is an approximation through near points.

Then, regardless the fact that f(0) = -2, we can see that as x approaches 0 from both sides, the value of the function approaches 4.

Thus, we can conclude that the limit of f(x) when x tends to zero is equal to 4.

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Answer: NO

Step-by-step explanation:

Adult tickets cost $27

Child tickets cost $18

$18 x 4 child tickets = $72 + $27 adult ticket = $99

Answer: The coordinates of a point in the plane are represented by a pair of values, (x, y), where x is the horizontal position and y is the vertical position.

When a point is reflected across the x-axis, the x-coordinate remains the same, but the sign of the y-coordinate changes. This is because the x-axis acts as a mirror, flipping the point over to the opposite side of the axis.

So, the coordinates of the reflected point would be (x, -y).

In summary, the x-coordinates of a point and its reflection across the x-axis are the same, while the y-coordinates are different (one is positive, and the other is negative).

Step-by-step explanation:

The minimum number of rotations required for a 3500 km race is 52,800 rotations.

This is calculated by dividing the total distance of the race, 3500 km, by the circumference of the wheel, which is 2πr, where r is the radius of the wheel. The radius of the wheel must be between 27.5 cm (half of 55 cm) and 37.5 cm (half of 75 cm). So, the minimum number of rotations is given by 3500/(23.14r), where r is the minimum radius of the wheel. Substituting in r = 27.5 cm, we get the minimum number of rotations required for a 3500 km race as 52,800.

To arrive at this result, we must first calculate the circumference of the wheel, which is given by 2πr, where r is the radius of the wheel. Since the diameter of the wheel must be between 55 cm and 75 cm, the radius of the wheel must be between 27.5 cm (half of 55 cm) and 37.5 cm (half of 75 cm).

We then divide the total distance of the race, 3500 km, by the circumference of the wheel, which is given by 2πr. Substituting in the minimum radius of the wheel, 27.5 cm, we get the minimum number of rotations required for a 3500 km race as 52,800.

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Answer:

density of apple juice

1.034-1.051g.cm‐³

Answer: (x = 6, y = -0.5)

Step-by-step explanation:

Substitute into one of the equations: 3(5 - 2y) + 2y = 17

Apply Multiplicative Distribution Law: 15 - 6y + 2y = 17

Rearrange unknown terms to the left side of the equation: -6y + 2y = 17 - 15

Combine like terms: -4y = 2

Divide both sides of the equation by the coefficient of variable: y = 2 / (-4)

Remove the parentheses: y = -2 / 4

Calculate the product or quotient:  y = -0.5

Substitute into one of the equations: x = 5 - 2 * (-0.5)

Remove the parentheses: x = 5 - 2 * -0.5

Calculate the product or quotient: x = 5 + 1

Calculate the sum or difference: x = 6

The solution of the system is: {x = 6, y = -0.5}

Hope this helps!

The correct matching of the given numbers is as follows:

Natural numbers, whole numbers, integers, rational numbers, and irrational numbers can all be classified as real numbers.

An imaginary number is created by multiplying a real number by i where i = (-1). To calculate the square root of negative values, we employ imaginary numbers. For instance, (√-7) Equals (-1) √7

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Answer:

x > 50

Step-by-step explanation:

[tex]\frac{x}{10}[/tex] > 5 ( multiply both sides by 10 to clear the fraction )

x > 50

In linear equation, 3437.5  feet - lbs is the work done to haul the anchor .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Anchor  weighing = 100 lbs

   given 3  lb/ft

  the combined weight  = 3( 25 -y ) + 100

                                 = 175 - 3y

    the workdone on small solution is = (175 - 3y)Δy

                      w = ∫₀²⁵ (175 - 3y) dy

                        = 175[y]²⁵₀- 3/2[y²]²⁵₀

                       = 175 [ 25 - 0 ] - 3/2 [ 25²- 0²]

                       = 3437.5  feet - lbs

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The proof that (n+5)^2(n+3)^2 is a multiple of 4 is below

We can prove that (n+5)^2(n+3)^2 is a multiple of 4 by showing that both (n+5)^2 and (n+3)^2 are multiples of 4.

From the question, we can see that the exponents of both factors is 2

When these exponents are added, we have

Sum = 2 + 2

Evaluate the sum

Sum = 4

4 is a multiple of 4

Hence,  (n+5)^2(n+3)^2 is a multiple of 4

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The perimeter of ABCD is, √18 + 5 + √29 + √10

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The diagram of ABCD is shown.

Now, The coordinate of the ABCD are,

⇒ A = (- 3, 2)

⇒ B = (0, 5)

⇒ C = (3, 1)

⇒ D = (-2, - 1)

Hence, Distance between A and B is,

⇒ f = √(- 3 - 0)² + (2 - 5)²

⇒ f = √9 + 9

⇒ f = √18

Distance between B and C is,

⇒ g = √(3 - 0)² + (1 - 5)²

⇒ g = √9 + 16

⇒ g = √25

⇒ g = 5

Distance between C and D is,

⇒ h = √(- 2 - 3)² + (- 1 - 1)²

⇒ h = √25 + 4

⇒ h = √29

Distance between D and A is,

⇒ i = √(- 3 + 2)² + (2 + 1)²

⇒ i = √1 + 9

⇒ i = √10

Hence, The perimeter of ABCD is,

⇒ f + g + h + i

⇒ √18 + 5 + √29 + √10

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Answer:

  4% and 8%

Step-by-step explanation:

You want to know the interest rates that yield $168 on investments of $2200 at one rate and $1000 at a rate 4% higher.

Let r represent the lower interest rate. Then x+0.04 is the higher rate, and the total interest earned is ...

  2200r +1000(r +0.04) = 168

Simplifying the equation, we have ...

  3200r +40 = 168

  3200r = 128 . . . . . . . . subtract 40

  r = 128/3200 = 0.04 = 4% . . . . . divide by the coefficient of r

The rates of interest on Lindays's investments were 4% and 8%.

Answer:

all real number

Step-by-step explanation:

domain are the value of x axis. as you can see the the graph goes for ever. there is no limitation. basically the domain of exponential graph are all really number.

Answer:

-1/2 is the answer of this question

P should stand for the population in a certain year. P = 97*(0.875) is the function to model the population change (year-2021).

P should stand for the population in a certain year. To simulate how the animal population changes over time, we can utilise a function. The 12.5% annual reduction rate will be considered by the function. This can be stated mathematically as P = 97*(0.875), which is how it will appear in the equation (year-2021). In this equation, the number 97 stands in for the population in 2021, and the number 0.875 denotes the 12.5% annual decline rate. The exponent (year 2021) represents the number of years that have passed since 2021, allowing the equation to take the population decline over a number of years into consideration. As a result, the equation can be used to determine the animal species' population at the start of a particular year.

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