Sharks can swim 45 miles per hour. How long would it take for the shark to swim 1 mile?

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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Answer:

4 laps

Step-by-step explanation:

A jogging trail has sides that measure

168 yards 2 feet,

175 yards, and

96 yards 1 foot.

total = 168+175+96 yards and 3 feet= 439 yd 3ft

1 yard = 3ft

so total 440yd

How many laps around the trail is equal to 1 mile (1,760 yards)?

1760/440 = 4laps

overload it by doing it again and again.

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

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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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

Jimmy  has five dollars more than three times Bethany has. Jimmy has $31.25.

A mathematical statement with two equal algebraic expressions is called an algebraic equation. Equations in algebra with only one variable are referred to as univariate equations, while equations with several variables are referred to as multivariate equations.

Let's say Jimmy has [tex]x[/tex] dollars.

Three times the amount of money Bethany has is [tex]3x[/tex].

Jimmy has 5 dollars more than three times what Bethany has,

so, [tex]x = 3x + 5[/tex]

The combined amount of money Jimmy and Bethany have is $130,

so, [tex]x + 3x +5= 130[/tex]

Combining like terms, [tex]4x = 125[/tex].

Dividing both sides by 4, [tex]x = 31.25[/tex]

So Jimmy has $31.25.

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Answer:

Jimmy have $98.75.

Step-by-step explanation:

let J=money Jimmy have

B= money Batheby have

therefore J = 5+3B.....................(1)

but J + B = $130.......................(2).

putting equation (1) into 2

5 + 3B + B = 130

4B = 130 - 5

4B = 125

4B/4 = 125/4

B = 31.25

therefore J = 5+ 3B = 5 + 3(31.25)

= 5 + 93.75

= $98.75.

therefore Jimmy have $98.75.

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:

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 ...

<95141404393>

Answer:

Step-by-step explanation:

890

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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Therefore, the distance across the river is approximately 283 feet (rounded to the nearest foot).

An equation is a mathematical statement that uses symbols, such as letters and numbers, to show that two expressions are equal. It typically consists of two sides separated by an equals sign. The expressions on both sides can contain variables, constants, functions, and operators, and the goal is often to solve for the value(s) of the variable(s) that make the equation true. Equations are used extensively in mathematics, science, engineering, and many other fields to model real-world phenomena, make predictions, and solve problems.

Here,

Without a diagram, it is difficult to determine the exact location and orientation of the points and lines. However, based on the information provided, we can use the Law of Sines to find the length of PR.

In triangle ROC, we have:

sin(CEO) = RO/OC

sin(CEO) = 165/330

sin(CEO) = 0.5

CEO = sin⁻¹(0.5)

CEO = 30 degrees

In triangle REO, we have:

sin(ERO) = RO/RE

sin(ERO) = 165/210

sin(ERO) = 0.7857

ERO = sin⁻¹(0.7857)

ERO = 51.06 degrees

Now, in triangle PER, we have:

sin(PER) / 210 = sin(ERO) / PR

Therefore, we can solve for PR:

PR = 210 * sin(ERO) / sin(PER)

PR = 210 * sin(51.06) / sin(180 - CEO - ERO)

Plugging in the values, we get:

PR = 210 * sin(51.06) / sin(99.94)

PR ≈ 283.2 feet

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Answer:

Step-by-step explanation:

Given

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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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:

The figures are similar.

Step-by-step explanation:

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

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]

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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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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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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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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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.

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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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).

By using synthetic division and the Remainder Theorem, we have found that f(-2) = -14, f(-1) = -7, f(0) = 7, f(1) = -6 and f(2) = -6.

Synthetic Division: Synthetic division is a shorthand method for dividing polynomials. It is used to divide a polynomial by a binomial of the form x - k, where k is a real number. To perform synthetic division, the coefficients of the polynomial are written in a row and divided by the denominator of the binomial.

To calculate f(-2), f(-1), f(0), f(1), f(2):

We will use synthetic division with the binomial x - k, where k = -2, -1, 0, 1, 2.

First, we will write the coefficients of the polynomial in a row:

7, -6, 3

For k = -2:

7|-2  -1  3

-2|-14  0  0

4  1  3

Therefore, f(-2) = -14.

For k = -1:

7|-1  -2  3

-1|-7  0  0

7  1  3

Therefore, f(-1) = -7.

For k = 0:

7|0  -1  3

0|7  0  0

7  -1  3

Therefore, f(0) = 7.

For k = 1:

7|1  0  3

1|7  -6  0

Therefore, f(1) = -6.

For k = 2:

7|2  1  3

2|14  -6  0

Therefore, f(2) = -6.

By using synthetic division and the Remainder Theorem, we have found that f(-2) = -14, f(-1) = -7, f(0) = 7, f(1) = -6 and f(2) = -6.

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Answer: 20 minutes

Step-by-step explanation:

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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