A jogging trail has sides that measure 168 yards 2 feet, 175 yards, and 96 yards 1 foot. How many laps around the trail is equal to 1 mile (1,760 yards)?

The solution is, center = ( 0,0) & coefficient = 3

The act or action of enlarging, expanding, or widening : the state of being dilated: such as. : the act or process of expanding (such as in extent or volume)

here, we have,

from the given figure,

we get,

length of MQ = 8.48

length of M'Q' = 2.82

so, dilation factor = 8.48/2.82

                             = 3

and, we get, the center of dilation = (0,0)

Hence, The solution is, center = ( 0,0) & coefficient = 3

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Answer: 5.83 units. please give brainliest

Step-by-step explanation: Using the distance formula, we can find the distance between the two points A(1, -5) and B(-4, -2):

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

d = sqrt((-4 - 1)^2 + (-2 - (-5))^2)

d = sqrt((-5)^2 + 3^2)

d = sqrt(25 + 9)

d = sqrt(34)

To the nearest hundredth, the length of line segment AB is approximately 5.83 units.

Answer:

Step-by-step explanation:

You want the number of liters of 25%, 45%, and 65% acid solution required to make a mixture that is 224 L of a 35% acid solution, using 3 times as much of the 65% solution as of the 45% solution.

There are numerous ways this mixing problem can be formulated. The calculator display in the attachment shows one of them: 3 equations in 3 unknowns.

Here, we choose to use one variable. Let x represent the amount of 45% solution. Then 3x is the amount of 65% solution, and (224 -4x) is the amount of 25% solution. The amount of acid in the final mix is ...

  0.25(224 -4x) + 0.45x + 0.65(3x) = 0.35·224

The equation can be simplified to ...

  1.4x +56 = 78.4

  1.4x = 22.4

  x = 16 . . . . . . . . . liters of 45% solution

  3x = 48 . . . . . . . . liters of 65% solution

  224 -4x = 224 -64 = 160 . . . . liters of 25% solution

The chemist should use ...

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Ther statement that is true regarding the application of Chebyshev's theorem and the Empirical Rule is B.Chebyshev's theorem works for symmetrical, bell-shaped distributions.

The Empirical Rule is an approximation that only works with data sets that have a relative frequency histogram with a bell-shaped distribution. The percentage of measurements that fall within one, two, and three standard deviations of the mean is estimated.

It is true that Chebyshev's Theorem holds true for all conceivable data sets. Both do not require a sample standard deviation for the data.

Therefore, option B is correct.

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An atom X has 3 protons in its nucleus. An atomic number of 3 corresponds to the element lithium (Li).

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

We can use Coulomb's law to predict the number of protons in X's nucleus. Coulomb's law states that the force of attraction between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.

⇒ F = k (q₁ q₂) / r²

Where, F is the force of attraction, k is the Coulomb constant (8.99 x 10⁹ Nm²/C²), q₁ and q₂ are the magnitudes of the charges, and r is the distance between them.

We can rearrange the equation to solve for the charge:

⇒ q₂ = (F * r²) / (k * q₁)

In this case, q1 is the charge on the electron, which is -1.60 x 10⁻¹⁹ C. The radius of atom X, r, is given, and the force of attraction, F, is also given.

So, we have:

⇒ q₂ = (2.2 x 10⁻⁸ N * (1.02 x 10⁻¹⁰ m)²) / (8.99 x 10⁹ Nm²/C^2 * -1.60 x 10⁻¹⁹ C)

Solving for q₂, we find that;

q₂ = +5.4 x 10⁻¹⁹ C.

This is the charge on the nucleus of atom X. The number of protons in the nucleus of atom X can be found by dividing the charge by the charge of a proton:

⇒ N = q₂ / qp

Where N is the number of protons and qp is the charge on a proton, which is +1.60 x 10⁻¹⁹ C.

So, we have:

N = (5.4 x 10⁻¹⁹ C) / (1.60 x 10⁻¹⁹ C) = 3.375

Hence, the number of protons must be a whole number, the closest whole number to 3.375 is 3. This means that atom X has 3 protons in its nucleus. The identity of atom X can be determined based on its atomic number, which is equal to the number of protons in its nucleus. An atomic number of 3 corresponds to the element lithium (Li).

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In this population of 100 individuals, approximately 49 individuals will have green hair due to the dominant allele CC and approximately 42 individuals will have green hair due to the dominant allele Cc. The total number of individuals with green hair is 49 + 42 = 91.

What is the quadratic equation?

A quadratic equation in one variable is a mathematical sentence of degree 2 that can be written in the following standard form. a+ bx + c = 0, where a, b, and c are real numbers and a 0.

The Hardy-Weinberg equilibrium is an idealized model of a population that assumes that the frequency of alleles remains constant from generation to generation in the absence of external forces.

According to this model, the frequency of a particular genotype can be calculated using the following formula:

p² + 2pq + q² = 1

where p is the frequency of the dominant allele (C) and q is the frequency of the recessive allele (c). In this case, p = 1 - q = 1 - 0.3 = 0.7, and q = 0.3.

The frequency of individuals with the genotype CC (green hair) is given by p², or 0.7² = 0.49.

The frequency of individuals with the genotype Cc (green hair) is given by 2pq, or 2 * 0.7 * 0.3 = 0.42.

Hence, in this population of 100 individuals, approximately 49 individuals will have green hair due to the dominant allele CC and approximately 42 individuals will have green hair due to the dominant allele Cc. The total number of individuals with green hair is 49 + 42 = 91.

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The exact length of the midsegment of the trapezoid is  √29 units.

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

The midsegment of a trapezoid is the line segment that connects the midpoints of the two non-parallel sides. Let's first find the midpoints of the sides SU and TV.

The midpoint of SU can be found as:

((Sx + Ux)/2, (Sy + Uy)/2) = ((-2 + 3)/2, (4 - 2)/2) = (1/2, 1)

Similarly, the midpoint of TV can be found as:

((Tx + Vx)/2, (Ty + Vy)/2) = ((-2 + 13)/2, (-4 + 10)/2) = (5.5, 3)

Now we can find the length of the midsegment that connects these two midpoints.

Distance=√(x₂-x₁)²+(y₂-y₁)²

So the length of the midsegment is:

d = √(5.5 -0.5)²+ (3 - 1)²)

= √25 + 4= = √29

Therefore, the exact length of the midsegment of the trapezoid is  √29 units.

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To graph the equation y = 12.3x, identify and locate the vertical and horizontal intercepts. To do this, set x equal to zero to find the vertical intercept, which is y = 12.3(0) = 0. Then, set y equal to zero to find the horizontal intercept, which is x = 0/12.3 = 0.

To graph the equation y = 12.3x, we need to identify and locate the vertical and horizontal intercepts. The vertical intercept is found by setting x equal to zero, which gives us y = 12.3(0) = 0. This means the vertical intercept is at the point (0,0). The horizontal intercept is found by setting y equal to zero, which gives us x = 0/12.3 = 0. This means the horizontal intercept is at the point (0,12.3). We can then plot these two points to graph the equation. Drawing a line through the points, we can see that the equation is a straight line that goes through the origin with a positive slope, meaning that as x increases, so does y. This line has a y-intercept of 0 and an x-intercept of 12.3.

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Answer:

Step-by-step explanation:

Given

The answer as a result of the numerical expression above is B) 1/36

This expression is rank number:

[tex]( {6}^{ - 4} ) {}^{ \frac{1}{2} } = 6 {}^{ - 2} = \frac{1}{ {6}^{2} } = \frac{1}{36}.

So the answer as a result of the numerical expression above is 1/36.

From these calculations it can be seen that the rank between what is inside the brackets and what is outside it can be multiplied.

In the question above the power of -4 multiplied by the power of ½ ( (-4×½) the result is -2.

So all that's left is 6⁻². Another form of 6⁻² is 1/6² or 1/36.

This refers to the exponential rule in mathematics, namely a⁻ⁿ can be written as 1/aⁿ.

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Answer:

5cm

Step-by-step explanation:

if the shorter wire = x

therefore the longer wire = x+4

[tex] x + x + 4 = 14[/tex]

Subtract 4 from both sides

[tex]x + x + 4 - 4 = 14 - 4[/tex]

[tex]x + x = 10[/tex]

[tex]2x = 10[/tex]

Divide both sides by 2

[tex] \frac{2x}{2} = \frac{10}{2} [/tex]

[tex]x = 5[/tex]

True, a contour line defines the outer edge or profile of an object, and can be used to suggest a volume in space.

It is the amount of space contained within the boundaries of an object and is typically represented by cubic units such as cubic centimeters (cm³), cubic meters (m³), or cubic inches (in³).

Volume can be calculated for various three-dimensional objects such as a cube, sphere, cylinder, or pyramid. The formula for finding the volume of an object depends on its shape. For example, the formula for the volume of a cube is V = s³, where s is the length of one of its sides. The formula for the volume of a cylinder is V = π²h, where r is the radius of the base, h is the height of the cylinder, and π is a mathematical constant approximately equal to 3.14.

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The capacity of her mixture in liters is 1.6 L

Capacity describes your ability to do something or the amount something can hold.

Given that, Jane mixes the juice in jug A with the water in jug B, we need to find that, what is the capacity of her mixture in liters,

We know that,

1 L = 1000 ml

Jug A = 400 × 1L / 1000 ml = 0.4 L

Jug B = 12 / 10 L = 1.2 L

Total = 0.4 + 1.2 = 1.6 L

Hence, the capacity of her mixture in liters is 1.6 L

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Answer:

The total of all three raises is $1,890. Jane's raise is $1,660 (4% of $41,400), John's raise is $1,980 (4.5% of $44,000), and Jack's raise is $1,250 (3% of $39,400).

The taxable income of the family is 1,15,37,000, the tax liability is given as  34,61,100.

Mr. B's taxable income calculation:

Income from Business: 75,00,000

Gift received: 6,00,000

Lottery winnings: 19,00,000

Maturity amount of life insurance: 32,00,000

Total Income: 1,32,00,000

Expenditures:

Family trip: 15,00,000

Gift to wife: 4,50,000

Life insurance premium: 50,000

Tuition fee: 50,000

PPF investment: 80,000

Medical test fee: 6,000

Health insurance premium: 27,000

Total Expenditures: 16,63,000

Taxable Income: 1,15,37,000 (Total Income - Total Expenditures)

Tax liability calculation:

Taxable Income Tax Rate Up to (in Rupees)

2.5 Lakhs NIL

2.5 Lakhs to 5 Lakhs 5% (12,500)

5 Lakhs to 7.5 Lakhs 10% (25,000)

7.5 Lakhs to 10 Lakhs 15% (37,500)

10 Lakhs to 12.5 Lakhs 20% (50,000)

12.5 Lakhs to 15 Lakhs 25% (62,500)

Above 15 Lakhs 30%

In this case, Mr. B's taxable income is 1,15,37,000, which falls in the tax bracket of above 15 Lakhs, so his tax liability would be 30% of 1,15,37,000 = 34,61,100.

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Answer:

Step-by-step explanation:

890

Answer:

x + 2y = 6

2y = -x -6

y = - 1/2 x - 3

From the equation, the y intercept is -3

Put y = 0,

-1/2 x -3 = 0

-1/2 x = 3

x = -6

Therefore, x intercept = -6

The total number of winning hands are 276.

Probability is defined as the ratio of favorable outcomes to all other possible outcomes of an event. The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes. The probability of an event can be calculated using the following formula.

Probability of an event = Number of favourable outcomes/Total number of outcomes = x/n.

In the given question,

If the first card drawn is a 10, then there are

[tex]P_9^2=\frac{9!}{(9-2)!} =9*8=72 hands[/tex]

There are 9 possible numbers if the second card is a 10, and there are 8 possible numbers if the third card, giving us,

[tex]9*8= 72 hands[/tex]

If the third card is 10 then there are 9 possible numbers for the first card and 8 possible numbers for

second card, it gives us

[tex]9*8= 72 hands[/tex]

And there are 5 odd cards, and it gives us:

[tex]P_5^3=\frac{5!}{(5-3)!} =5*4*3=60 hands[/tex]

So, we have that in total we have

72+72+72+60=276 winning hands.

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Answer:

$13,488.50

Step-by-step explanation:

annual rate 6%

so every month = 6/12 = 0.5%

compounding monthly so every month the money grows at (1+0.5%)

for 5 years, it's 60 months

10,000 *  (1+0.5%)^60 =  $13,488.50

Answer: 36

Step-by-step explanation:

to find the length, find the hypotenuse of a triangle formed by the x-axis and the distance the parallelogram is from the x-axis.

hypotenuse= [tex]a^{2}+b^{2} =c^{2}[/tex]

the distance from -6 to -3 is 3 units

the distance from 0 to 4 is 4 units

[tex]3^{2} +4^{2} =9+16=25[/tex]

then [tex]\sqrt{25} =5[/tex]

therefore the length of the parallelogram is 5 units

repeat on other side

the distance from -3 and 9 is 12 units

the distance from 0 and 5 is 5 units

[tex]12^{2} +5^{2} =144+25=169[/tex]

then [tex]\sqrt{169} =13[/tex]

therefore the width of the parallelogram is 13 units

now to find the perimeter add all side lengths of the given shape

since parallelograms have equal lengths and widths add 13+13+5+5

therefore the perimeter of the parallelogram is 36

Answer:

The figures are similar.

Step-by-step explanation:

The scale factor is 2.  The transformation is a a dilation.

The solution is,  1/3 ÷ 6, expression shows how much of the pan each person gets.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

wen and five friends equally share 1/3 of a pan of snack bars.

so, we get,

the expression is 1/3 ÷ 6

This is because there are 6 friends in all and you are splitting 1/3 of the pan snack bars to each of them.

So, what your splitting/cutting/dividing would be the dividend (1/3) and then the friends would be the divisor (6)

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Answer:

Step-by-step explanation:

To solve this - determine how long it takes the acron to fall 12 feet.

At that point it will be 1 foot above ground.  13-1 = 12 so you are solving for how long it takes for the acorn to fall 12 feet.

Make a proportion:  

seconds    =    1     =        x

distance        4.8            12

If the acorn falls 4.8 feet every second, how long does it take to fall 12 feet, which is one foot above the ground.

Cross multiply:   4.8x= 12 (1)

                           4.8x = 12

divide each side by 4.8

                          4.8x/4.8 = 12/4.8

                              x       =   2.5

It takes 2.5 seconds to be one foot above the ground or fall 12 feet.

The complete question

A model rocket is launched with an initial upward velocity of 50m/s. The rocket's height h (in meters) after t seconds is given by the following. h=50t-5t².

Find all values of t for which the rockets height is 20 meters.

The values of t for which the rockets height is 20 meter are, (10 + 2√21) / 2  and (10 - 2√21) / 2

Velocity is a vector quantity that represents the rate of change of an object's position. It is defined as the derivative of the position vector with respect to time and has units of meters per second (m/s). Velocity includes both speed and direction, and is an important concept in physics and engineering.

We can find the values of t for which the rocket's height is 20 meters by setting h equal to 20 and solving for t.

h = 50t - 5t² = 20

Expanding the equation, we have:

50t - 5t² = 20

Adding 5t² to both sides:

50t = 20 + 5t²

Dividing by 5 both the sides,

10t = 4 + t²

t² - 10t + 4 = 0

t = (10 + 2√21) / 2

and t = (10 - 2√21) / 2

So the values of t for which the rocket's height is 20 meters are

(10 + 2√21) / 2  and (10 - 2√21) / 2

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Based on the given information:

From the case we know that the cost of rent a truck was charged by 2 rules:

Cost per truck = fixed cost = $22.95

Cost per miles distance = variable cost = $0.72 per mile

Both costs can be formulated as a linear equation:

C(d) = 22.95 + 0.72d

where we take the fixed cost of $22.95 as the y-intercept and the variable cost of $0.72 per mile as the slope of the line.

Based on our linear equation, we can try to find the cost needed to rent a truck and drive it for 15 miles:

C(15) = 22.95 + 0.72(15)

C(15) = 22.95 + 10.8

C(15) = $33.75

We can use the same approach to find the available distance for our budget of $110:

C(d) = 22.95 + 0.72d

110 = 22.95 + 0.72d

0.72d = 87.05

d = 120.9

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The new solid's surface area, which is 490 cm², is created by combining two identical cubes, each of which has a surface area of 294 cm².

The total area of a cube's faces that cover it is the surface area of the object. The cube's surface area is calculated as six times the square of its side lengths. 6a², where an is the cube's side length, serves as its representation. In essence, it is the overall surface area.

Total surface area of a cube = 6a², where a is the length of each of the sides.

Let the surface area of each identical cube = 294 cm²

The length of each side be

6a² = 294

simplifying the above equation, we get

a² = 294/6

a² = 49

a = √49

a = 7 cm

Surface area of the new solid

= surface area of the two identical cubes - 2(area of the surface where both are joined)

Surface area of the new solid = 2(294) - 2(7²) = 490 cm²

Therefore, the surface area of the new solid be 490 cm².

The complete question is;

Two identical rectangular prisms and two identical cubes are joined. Answer the questions to find the new solid’s surface area. The numbers are 9 and 4.

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Answer: 20 minutes

Step-by-step explanation:

overload it by doing it again and again.