Solve for l if V = 120 w = 5 and h = 4

It takes the toy car 2.43 seconds to fall to the bottom floor,  answer choice is B. 9/4 seconds, which is equal to 2.25 seconds.

An equation is a mathematical statement that asserts that two expressions are equal. An equation consists of two sides, the left-hand side and the right-hand side, separated by an equal sign (=).

For example, 2x + 5 = 11 is an equation, where the left-hand side is 2x + 5 and the right-hand side is 11. This equation asserts that the expression 2x + 5 is equal to 11, and the value of x can be determined by solving for x.

Equations can be simple or complex, and they can involve one or more variables. They can also be linear or nonlinear, depending on the nature of the expressions involved.

Solving an equation involves finding the values of the variables that make the equation true. This may involve applying algebraic operations and simplification techniques to isolate the variable on one side of the equation.

Equations are used in many areas of mathematics, science, engineering, and economics, and they provide a powerful tool for modeling and analyzing real-world situations. They are also used extensively in computer programming and cryptography, where they play a critical role in the development of algorithms and data encryption methods.

We have the equation [tex]h = 94 - 16t^2[/tex], where h is the height of the toy car in feet and t is the time in seconds.

When the toy car reaches the bottom floor, its height will be h = 0. So we can set the equation equal to 0 and solve for t:

[tex]0 = 94 - 16t^216t^2 = 94t^2 = 94/16[/tex]

[tex]t = \sqrt{(94/16)} = \sqrt{(23.5/4)} = 2.43 seconds[/tex] (rounded to two decimal places)

Therefore, it takes the toy car 2.43 seconds to fall to the bottom floor.

The closest answer choice is B. 9/4 seconds, which is equal to 2.25 seconds.

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Answer:

37

Step-by-step explanation:

2x - (-4x + 5b); x = 2; b = -5

2(2) - (-4 × 2 + 5 (-5)) = 4 - (-8 - 25) = 37

The angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.

A triangle is a closed geometric shape with three sides, three angles, and three line segments. Three non-collinear points are joined by line segments to create the simplest polygon, which has three non-collinear points.

Triangles can be categorized according to the size of their sides and angles. Triangles can be categorized as equilateral (all sides are equal in length), isosceles (both sides are equal in length), or scalene based on their sides (all sides are different in length). Triangles can be categorized as acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is greater than 90 degrees) (one angle is exactly 90 degrees).

In any triangle, the sum of the three interior angles is always 180 degrees. Therefore, we can write:

a + b + c = 180

Substituting the given values, we get:

(6x-1) + 20 + (x+14) = 180

Simplifying and solving for x, we get:

7x + 33 = 180

7x = 147

x = 21

Now that we have the value of x, we can substitute it back into the expressions for the angles to find their values:

angle a = (6x-1) = (6*21-1) = 125 degrees

angle b = 20 degrees

angle c = (x+14) = (21+14) = 35 degrees

Therefore, the angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.

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For the given function f(x) = cos x,  f '(x) = -sin x.

By the definition of the derivative, this means that -sin x provides the rate of change of cos x at a specific angle.

What is meant by the derivative of a function?

The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. It is described as the fluctuating rate at which a function changes in relation to an independent variable. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilised. The sensitivity of the dependent variable to the independent variable is assessed using the derivative. Calculus's core tool is derivative.

We are given the function f(x) = cos x

The derivative of cos x is -sin x.

That is, f '(x) = -sin x

Therefore, by definition of the derivative, this means that -sin x provides the rate of change of cos x at a specific angle.

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Answer:

1st one

Step-by-step explanation:

Answer: A. (2/5,-3)

Step-by-step explanation:

in order to find the solution to the set of equations, you need to find one variable first, lets fing y first

10x+3y=-5

10x = -5 - 3y

x = (-5 -3y)/10

substitute this in for x in the other equation

-5((-5 - 3y)/10) -4y = 10

(25 + 15y)/10 -4y = 10

25/10 + 15y/10 -4y = 10

make all fractions on the left side

25/10 + 15y/10 - 40y/10 = 10

combine

25/10 -25y/10 = 10

multiply both sides by 10 to get rid of the denominator

25 - 25y = 100

combine like terms

-25y = 75

divide

y = -3

plug y into the first equation to find x

10x + 3(-3) = -5

10x -9 = -5

10x = 4

x = 4/10

simplify

x = 2/5

hope this helps!

Answer:

Step-by-step explanation:

To find the left-hand derivative of f at x = 4, we need to evaluate:

f′−(4) = limh→0−f(4+h)−f(4)h

Since f(x) = 0 for x ≤ 0 and f(x) = 5 - x for 0 < x < 5, we have:

f(4 + h) = 0 for h < -4

f(4 + h) = 5 - (4 + h) = 1 - h for -4 < h < 1

f(4 + h) = undefined for h > 1

Therefore, we can rewrite the limit as:

f′−(4) = limh→0−f(4+h)−f(4)h = limh→0−(1 - h) - 0h = -1

To find the right-hand derivative of f at x = 4, we need to evaluate:

f′+(4) = limh→0+f(4+h)−f(4)h

Using the same reasoning as before, we can rewrite the limit as:

f′+(4) = limh→0+(5 - (4 + h)) - 0h = -1

Since the left-hand derivative and the right-hand derivative are equal, we can conclude that f'(4) exists and is equal to:

f'(4) = f′−(4) = f′+(4) = -1

Therefore, the derivative of f at x = 4 is -1.

The equation is  (4.5-0.7)/5 and length of each piece is 0.74

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

He has a piece of wood that is 4.5 feet long.

After cutting five equal pieces of wood from it, he has 0.7 feet of wood left over

an equation that could be used to determine the length of each of the five pieces of wood he cut

legth of each piece is = (4.5-0.7)/5

The total length is 4.5  and the leftover is 0.7, so used wood is total minus left ove

Length of each piece is used woof by number if pieces

(4.5 - 0.7)/5 = 3.7/5 = 0.74

Therefore, the equation is  (4.5-0.7)/5 and legth of each piece is 0.74

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The factorization of the polynomial is (x - 7)(x + 6). Option C is the correct answer.

The breaking or breakdown of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication yields the original number, matrix, etc., is known as factorization or factoring in mathematics.

The given polynomial is:

x² - x - 42 = 0

Expand the quadratic equation:

x² + 6x - 7x - 42 = 0

Take the common terms out from the equation:

x(x + 6) - 7(x + 6) = 0

(x - 7)(x + 6) = 0

Hence, the factorization of the polynomial is (x - 7)(x + 6). Option C is the correct answer.

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The first node in set 1 should represent the element.

For each potential value in set 2, create a branch.

Create a new node to represent the following set 1 element at the end of each branch.

Steps 2-4 must be repeated for each additional Set 1 component.

All potential outcomes are represented by the final nodes.

The appropriate line of best fit for the scatter plot is y hat equals 67 hundredths times x plus 4 and 5 hundredths.

The number is a mathematical entity used to represent a computer's magnitude it can be a symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three, or eight numbers are used to verify the context including counting measuring and computing.

This line of best fit indicates that the number of households with cable television will increase by 67 hundredths (or 0.67) each year. This line of best fit is based on the data points on the scatter plot, which suggest that the number of households with cable television has been steadily increasing over the years.

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Answer:

0.1369

Step-by-step explanation:

(37/100)^2=0.1369

Answer:

Step-by-step explanation:

the answer is

B

and
C

Answer:

1110

Step-by-step explanation:

Answer:

pretty sure its "A"

Step-by-step explanation:

Answer:

The answer is (A) 8.1%.

Step-by-step explanation:

The probability of flipping a coin and getting heads is 1/2 or 0.5. Assuming the coin is fair, the probability of getting heads 4 times in 11 flips is given by the binomial probability formula:

P(4 heads in 11 flips) = (11 choose 4) * (0.5)^4 * (0.5)^(11-4) = 330 * 0.5^11

Using a calculator, we get:

P(4 heads in 11 flips) ≈ 8.1%

Therefore, the answer is (A) 8.1%.

Answer: One foot is equal to 12 inches, and since 1 inch is equal to 2.54 centimeters, we have:

1 foot = 12 inches = 12 x 2.54 cm = 30.48 cm

So the length of the flat bar is 30.48 cm. Multiplying this length by the price per cm, we get:

30.48 cm x 2 pesos/cm = 60.96 pesos

Therefore, we need 60.96 pesos to buy a flat bar of length 1 foot at a price of 2 pesos per cm.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To determine how many yards of fabric Charles has left, we need to subtract the total amount of fabric used for the costume, pillows, and bag from the initial amount of fabric (m yards). The total amount of fabric used is:

Now, we can subtract the total used fabric from the initial amount of fabric:

The correct expressions that show how many yards of fabric Charles has left are:

So, the correct options are (A), (C), (E), (F), (G), and (H).

________________________________________________________

Answer: 6 3/4 I hope this helps

Step-by-step explanation:

27/4

Convert the improper fraction into a mixed number

6 3/4

Mixed number-A number written as a whole number and a fraction.

Answer:

Step-by-step explanation:

a) The slope of the line passing through the points (5,6) and (-1,6) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (5,6) and (x2, y2) = (-1,6).

m = (6 - 6) / (-1 - 5) = 0 / -6 = 0

Therefore, the slope of the line is 0.

b) The slope of the line passing through the points (3,-2) and (3,-1) cannot be calculated using the previous formula since the points have the same x coordinate. This means that the line is vertical and therefore its slope is infinite (or undefined).

c) The slope of the line passing through the points (2,2) and (-5,2) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (2,2) and (x2, y2) = (-5,2).

m = (2 - 2) / (-5 - 2) = 0 / -7 = 0

Therefore, the slope of the line is 0.

d) The slope of the line passing through the points (9,-2) and (-7,-2) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (9,-2) and (x2, y2) = (-7,-2).

m = (-2 - (-2)) / (-7 - 9) = 0 / -16 = 0

Therefore, the slope of the line is 0.

e) The slope of the line passing through the points (-8,22) and (1,4) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-8,22) and (x2, y2) = (1,4).

m = (4 - 22) / (1 - (-8)) = -18 / 9 = -2

Therefore, the slope of the line is -2.

f) Since we know the slope m = 2 and one of the points is (3,6), we can use the formula:

y - y1 = m(x - x1)

where (x1, y1) = (3,6). Substituting m and (x1, y1) into the formula, we get:

y - 6 = 2(x - 3)

Expanding the formula and solving for y, we get:

y = 2x - 6 + 6

y = 2x

Therefore, the y-coordinate of the second point is y = 2(4) = 8. The second point is (4,8).

y = 14/11 x is the required equation. Option Cis correct

If the variable y varies directly with x, this is expressed as:

y = kx

where

k is the constant of proportionality

Given that x = 11 and y = 14, hence;

k = y/x

k = 14/11

Substitute k into the original equation

y = kx

y = 14/11 x

Hence the required equation from the given information is y = 14/11 x

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The system of linear equations is solved by finding x = 2 and y = -4, making the solution (2, -4).

To find the solution to the system of linear equations,

find the values of x and y that satisfy both equations simultaneously.

The equations are,

y = -3x + 2

y = x - 6

To find the solution,  set the right-hand sides of both equations equal to each other:

-3x + 2 = x - 6

Now, let's solve for x:

-3x - x = -6 - 2

-4x = -8

x = -8 / -4

x = 2

Now that  the value of x, we can find y by substituting x back into one of the equations.

Let's use the second equation:

y = 2 - 6

y = -4

Therefore, the solution to the system of linear equations is equal to option A. (2, -4).

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The probability that he will make both free throws is 0.84.

What exactly is the meaning of probability?

Probability expresses the possibility of an event. This branch of mathematics studies the occurrence of a random event. The value ranges between 0 and 1. Probability is used in mathematics to anticipate the possibility of events occurring.

Probability refers to the likelihood of something occurring. This fundamental premise of probability theory is used by the probability distribution. We must first know the entire number of possibilities before we can assess the possibility of an event occurring.

P(E) is the probability of an event occurring divided by the total number of outcomes.

Now,

Given that player makes 92% of freethrows

that means p(making free throws)=92/100

=23/25

so making two free throws probability will be =23*23/25*25

=529/625

=0.84

Hence,

           The probability that he will make both free throws is 0.84.

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Answer:

The expected growth rate for the company's stock price is 9.7%. This is calculated by subtracting the dividend yield (3.40/53.50 = 0.0635) from the required return (13%).

The next step on solving completing square is: 5 (x² + 4x) = 7 and 5(x² + 4x + 4) = 7 + 20. So, these steps could he use to solve the quadratic equation by completing the square.

Any equation in algebra that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known values, and where a ≠ 0 is true is known as a quadratic equation.

Case 1:

Given equation becomes:

5x² + 20x - 7 = 0

Firstly, we will add of 7 in both sides:

5x² + 20x - 7 + 7 = 0 + 7

Now, same variable of opposite sign is cancelled:

5x² + 20x = 7

Now, taking 5 common from left side:

5 (x² + 4x) = 7

Case 2:

Given equation becomes:

5x² + 20x - 7 = 0

Firstly, we will add of 7 in both sides:

5x² + 20x - 7 + 7 = 0 + 7

Now, same variable of opposite sign is cancelled:

5x² + 20x = 7

Now, we will add of 20 in both sides

5x² + 20x + 20 = 7 + 20

Now, taking common of 5 from left side:

5(x² + 4x + 4) = 7 + 20

So, The next step on solving completing square is: 5 (x² + 4x) = 7 and 5(x² + 4x + 4) = 7 + 20

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a) The ball is at 5 feet height when it leaves the child's hand

b)  The maximum height of the ball is 131 feet

c) 84.825 ft  far from the child, the ball strike the ground

What is a quadratic equation?

A quadratic equation is a second-order polynomial equation with a single variable such as x, where ax²+bx+c=0. with a ≠ 0 . Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.

(a)

At the beginning when the ball leaves the hand of the child, the horizontal distance was 0, so putting x=0 we can get the height of the ball.

at time zero, t=0, the distance is 5 feet, so the ball is at 5 feet height

(b)

the max occurs at the average of the solutions, which is 28.

or -b/2a = -6/(2*-1/14) = -6/ (-1/7) = 42 ft

-(1/14)*42^2 +6*42 + 5 = 131

so the max height is 131 feet after 42 feet

(c)

(-1/14) x^2 + 6x + 5 =0

x^2 - 84x - 70 = 0 <--- after multiplied by -14

x = 84.825, x = -0.825

the ball will hit the ground at (56 + sqrt(3416)) / 2 = 84.825 ft

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The probability that the random sample of 100 male students has a mean gpa greater than 3. 42 is 0.9452.

A statistic known as the standard deviation is used to describe how volatile or dispersed a group of numerical values is. While a big standard deviation denotes that the values are scattered across a wider range, a low standard deviation indicates that the values tend to be close to the set mean.

From the given information, a scores random sample of 100 male students is selected and the GPA for each student is calculated which follows approximately normal with a mean of 3.5 and standard deviation of 0.5. That is,

µ = 3. 5 and σ = 0. 5

and the random sample of 100 male students has a mean GPA 3.42 is considered.

The z-score value is,

Z=( 3.42-3.5)/ (0.5/√100)

Z= -0.08/0.05

Z=-1.6

The value of z-score is obtained by taking the difference of x and µ. Then the resulting value is divided with the standard deviation by sample size.

The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is obtained below:

The required probability is,

P(X>3.42)=P(z>-1.6)

= 1- P(Z≤-1.6)

From the “standard normal table”, the area to the left of Z=-1.6 is 0.0548.

P(X>3.42)= 1- P(Z≤-1.6)

=1-0.0548

=0.9452

The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is 0.9452.

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The cubic root of z = -27 is -3

A real cube and tree roots may be the first images that come to mind when we hear the terms "cube" and "root." Is it not? Well, the concept is the same. Root refers to the main source or starting point. So, all we need to do is consider "which number's cube should be taken to get the given number." The cube root definition in mathematics is expressed as The cube root is the quantity that must be three times multiplied to yield the initial quantity. Let's look at the cube root equation: ∛x = y, where y is the cube root of x. Every number with a little 3 inscribed on it can be represented by the radical sign as the cube root symbol.

In this problem, the cubic root of z = -27 can be calculated as;

z = -∛-27

z = -3

This is because 27 is a perfect cube

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The values of k for which 2x² + kx - 5 can be factored as the product of two linear factors with integer coefficients are k = 3, 1, and 9.

What is a linear factor?

A linear factor is a polynomial of degree one, which means it has one variable raised to the first power and a constant coefficient. In other words, it is an expression of the form ax + b, where a and b are constants and x is the variable.

We can factor the quadratic 2x² + kx - 5 into the product of two linear factors with integer coefficients if and only if its discriminant is a perfect square.

The discriminant of the quadratic equation ax² + bx + c = 0 is given by the expression b² - 4ac. In this case, a = 2, b = k, and c = -5. Therefore, the discriminant is:

b² - 4ac = k² - 4(2)(-5) = k² + 40

For the quadratic to be factored into two linear factors with integer coefficients, k² + 40 must be a perfect square.

One way to proceed is to list the perfect squares that are 40 greater than a square, and see if k is one of the corresponding values. We can do this by solving the equation:

k² + 40 = m²

where m is an integer. Rearranging, we get:

k² - m² = -40

This is a difference of squares, so we can factor it:

(k + m)(k - m) = -40

We now need to find integer values of k and m that satisfy this equation. We can do this by considering all possible pairs of factors of -40 and solving for k and m.

The pairs of factors of -40 are:

(-1, 40), (-2, 20), (-4, 10), (-5, 8)

For each pair, we can solve the system of equations:

k + m = a

k - m = b

where a and b are the two factors in the pair. Adding these equations, we get:

2k = a + b

Subtracting them, we get:

2m = a - b

Solving for k and m, we obtain:

k = (a + b)/2

m = (a - b)/2

We can now check if the values of k and m are integers and if they satisfy the original equation.

For example, if we take the pair (-1, 40), we get:

k + m = -1

k - m = 40

Adding these equations, we get:

2k = 39

This implies that k = 39/2, which is not an integer, so this pair does not work.

Trying the other pairs, we find that:

(-2, 20) gives k = 9 and m = 11, which works

(-4, 10) gives k = 3 and m = 7, which works

(-5, 8) gives k = 1 and m = 3, which works

Therefore, the values of k for which 2x² + kx - 5 can be factored as the product of two linear factors with integer coefficients are k = 3, 1, and 9.

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Answer:

Step-by-step explanation:

here is a step by step answer:

A. To determine the surface area of the warehouse:

Identify the dimensions of each side of the warehouse. In this case, we know that the sides are 17 ft, 25 ft, and 33 ft in length, and the height is 10 ft.

Calculate the area of each side by multiplying the length and height. For example, the area of the first side is 17 ft x 10 ft = 170 sq ft.

Add up the areas of all the sides to get the total surface area of the warehouse. In this case, the total surface area is 170 + 250 + 330 = 750 sq ft.

B. To determine the area of the surfaces that need siding:

Since all sides of the warehouse need to be covered with siding, the area of the surfaces that need siding is equal to the total surface area of the warehouse. In this case, we calculated the total surface area to be 750 sq ft.

C. To determine how many pieces of siding need to be purchased:

Identify the size of each piece of siding. In this case, we know that each piece of siding is 4 ¾ inches x 24 inches.

Convert the size of each piece of siding to square feet. To do this, we can divide the length and width by 12 to convert to feet, and then multiply the two dimensions to get the area. In this case, 4 ¾ inches is approximately 0.3958 feet, and 24 inches is 2 feet, so the area of each piece of siding is approximately 0.7916 sq ft.

Divide the total surface area of the warehouse by the area of each piece of siding to get the number of pieces needed. In this case, we calculated that the total surface area is 750 sq ft, and each piece of siding covers approximately 0.7916 sq ft. So, the number of pieces needed is 750 sq ft ÷ 0.7916 sq ft/piece = 946.84 pieces. We must round up to the nearest whole number because we can't purchase a fraction of a piece of siding. So, we need to purchase 947 pieces of siding.

D. To determine the approximate cost of siding needed to cover the outside of the warehouse:

Identify the price per piece of siding. In this case, we know that the siding is priced at $22.65 per piece.

Multiply the number of pieces of siding needed by the price per piece to get the total cost of siding. In this case, we calculated that we need 947 pieces of siding, so the total cost of siding is 947 x $22.65 = $21,465.55. So, the approximate cost of siding needed to cover the outside of the warehouse is $21,465.55.

The option is (B) The entire solution region is viable is correct when both the inequalities are solved.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

Let's first translate the given information into mathematical inequalities -

The perimeter of the tabletop to be no more than 28 feet -

Perimeter = 2(length + width) ≤ 28

The length of the tabletop to be greater than or equal to the square of 2 feet less than its width -

Length ≥ (Width - 2)²

We can combine these two inequalities to form the system -

2(length + width) ≤ 28

Length ≥ (Width - 2)²

Now, let's solve for y in terms of x (so that we can graph the solution region) -

2(y + x) ≤ 28

y ≥ (x - 2)²

Simplifying the first inequality -

y ≤ -x + 14

Now graph both the inequalities -

The viable solutions are the points that satisfy both inequalities, which lie in the shaded region above.

Therefore, there is no part of the solution region that includes negative length or negative width.

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