The flower box is 5 ft​ long, and its ends are in the shape of a trapezoid. The upper and lower bases of the trapezoid measure 18 in. and 10​ in., respectively, and the height is 9 in. Find the volume of the flower box.

Answer:

Step-by-step explanation:

(8 x 100000) + (0 x 10000) + (4 x 1000) + (0 x 100) + (8 x 10) + (2 x 1) = 804082

The probability of P(A AND B) when Josh visit his aunt's house is 0.36.

Probability is the likelihood that an event will occur or take place.

Let A = the event that he walks his dog at his aunt's house

Let B = the event that he plays darts at his aunt's house.

When A and B are independent events with P(A)=0.9 and P(B)=0.4, the probability of P(A AND B) will be:

= P(A) × P(B)

= 0.9 × 0.4

= 0.36

The probability is 0.36.

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The height of the 5.2 feet person in centimeters is 158.496 cm.

A conversion factor must be added, subtracted, multiplied, or divided throughout the multi-step process of unit conversion. Additionally, selecting the appropriate number of significant digits and rounding may be necessary.

Different conversion units are used to quantify various measurements. By definition, unit conversion is the process of converting two measures of the same quantity between distinct units by multiplying or dividing them.

In mathematics, conversion is the process of changing a value's form, such as from millimeters to inches or liters to gallons. Units are used for measurements of length, weight, capacity, temperature, and speed.

Given,

Height of a person = 5.2 feet.

The conversion between inches and centimeters must also be included.

First, convert feet to inches.

1 foot = 12 inches

Converting the given height to inches,

Height = 5.2 × 12

= 62.4 inches

Now, we will convert the height into centimeters,

To convert, we will multiply by 2.54

Height = 62.4 × 2.54

= 158.496 cm

Therefore, the height of the person in centimeters is 158.496 cm

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Answer:

7x+10y=3

Step-by-step explanation:

Standard Form= Ax+By=c

Distribute first

4y-5x=12x-6y+3

Add 6y

10y-5x=12x+3

Add 12x

7x+10y=3

Answer:

58%

Step-by-step explanation:

35/60=0.58333=58/100=58%

Answer: x=16

Step-by-step explanation: 18=2x-14

32=2x

x= 16

The composition f(x) - g(x) has its value to be 12x

The definitions of the functions are given as

f(x) = (x - 3)²

Also, we have the definition of another functions to be given as

g(x) = (x + 3)²

To find the composition f(x) - g(x), we make use of the following equation

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

So, we have the following equation

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

Substitute the known values in the above equation

So, we have the following equation

f(x) - g(x) = (x + 3)² - (x - 3)²

Apply the differece of two squares rules

So, we have

f(x) - g(x) = (x + 3 + x - 3)(x + 3 - x + 3)

So, we have

f(x) - g(x) = (2x)(6)

This gives

f(x) - g(x) = 12x

Hence, the value of the composition is f(x) - g(x) = 12x

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Answer:

so basically u do that and then u do that and then

Step-by-step explanation:

8

The value of constant C is 50.

Equations with a maximum degree of one are referred to as linear equations. According to this rule, a variable in a linear equation cannot have an exponent greater than 1.

A linear equation's graph is always depicted as a straight line. There are linear equations for one variable and two variables, respectively.

Given, the linear equation is 12.5x+5y = C

Here, constant C.

Consider one points from given table x = -2 and y = 15,

Putting the value of x and y,

C = 12.5×(-2) + 5×15

   = -25 + 75

   = 50

For point, x = 0 and y = 10,

Putting the value of x and y,

C = 12.5×0 + 5×10

   = 50

For point, x = 2 and y = 5,

Putting the value of x and y,

C = 12.5×2 + 5×5

   = 25 + 25

   = 50

Given, x = 4 and y = 0,

Putting the value of x and y,

C = 12.5×4 + 5×0

   = 50

Therefore, the value of constant C was found to be 50.

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Answer:

5.8 hours

Step-by-step explanation:

First, you just plug it the given information.

Turn the equation to t=d/r by dividing the rate by both sides.

Plug it in 348miles/ 60 miles per hour

It'll take 5.8 hours for the car to travel 348 miles at the rate of 60 miles per hour.

Answer: n is greater than m

Step-by-step explanation:

if m=-1/2 then that means its -.50 and n=-1/3 meaning its -.333(...)

so n is greater (remember its negative so higher numbers are actually lesser in value)

Hope this helped... :)

Answer:

Step-by-step explanation:

You want to know whether the pairs of equations describe lines that are parallel, perpendicular, or neither.

Parallel lines have the same slope. When the equations are written in slope-intercept form, the coefficients of x are identical.

Perpendicular lines have opposite reciprocal slopes. When the equations are written in slope-intercept form, the product of the x-coefficients is -1.

Solving the first equation for y gives ...

  y = 2x +2

The x-coefficients are 2 and -2, so the lines are neither parallel nor perpendicular.

Solving the first equation for y gives ...

  y = 2/4x -1 = 1/2x -1

The x-coefficients are 1/2 and -2, which have a product of -1. These lines are perpendicular.

Solving the second equation for y gives ...

  y = 2x -7/2

The x-coefficients are 2 and 2, which are identical. These lines are parallel.

Answer:

Step-by-step explanation:

Answer:

One solution: x =21.6

Step-by-step explanation:

Equation

12x + 6 = 14(2x – 24)                    Remove the brackets

Solution

12x + 6 = 28x - 336                      Add 336 to both sides.

12x + 6+336 = 28x - 336             Combine

12x + 342 = 28x -336+336        

12x + 342 = 28x                            Subtract 12x from both sides.

12x-12x + 342 = 28x - 12x             Combine

342 = 16x                                      Divide by 16

342/16 = 16x/16

21.6=x  

Using percentages, the answer to all the subparts are shown:

So, calculate the percentages as follows:

(A) % who scored between 46 and 106:

Then,

Rounding off: 67% approx

(B) % who scored less than 46:

Then,

Rounding off: 17% approx

(C) % who scored between 61 and 91:

Then,

Rounding off: 33% approx

(D) % who scored between 76 and 121:

Then,

Therefore, using percentages, the answer to all the subparts are shown:

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Answer:

3???

Step-by-step explanation:

The type of angles have the same measure after being rotated, reflected, or translated in a coordinate plane is a I. II. and III.

Transformation is a term used in mathematics to refer to the movements made by objects.

Transformation is basically of two major divisions

Non rigid transformation are the transformation where the dimension or size of the object will be different from the image, example is dilation

In rigid transformation, the dimensions of the object is maintained through out the transformation examples of rigid transformation are

Since the transformation types mentioned are all rigid transformation hence all the angles will remain same

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The integer +3 describes the statement, 3 inches above average.

What is an average?

A single number chosen to represent a group of numbers is called an average, and it is typically calculated by dividing the total number of numbers in the group by the number of numbers in the group. As an illustration, the sum of the integers 2, 3, 4, 7, and 9 is 5.

One point in the average refers to the amount of 1 inch.

If the average is above 3 inches, it means that the value of the average is above 3 inches. It further implies that the total value has gained 3 inches on that average.

Inches mainly describe the gains and losses in short-time investments. A positive sign (+) shows the above average, and a negative sign (-) represents the below average.

Therefore, the integer +3 describes the statement, 3 inches above average.

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The correlation coefficient when there is a study of bone density on 5 random women is -0.909.

It is the statistical measure of the strength of the linear relationship that's between two variables. The correlation coefficient is calculated by calculating the covariance of the variables and dividing that number by the product of the standard deviations of those variables.

The steps for calculating the correlation coefficient are as follows:

The statistical software was used and the values include

Dependent variable = y

Independent variable = x

It should be noted that linear regression has an equation that is in the form of Y = a + bx. The equation is y = 451.674 - 2.051. This was gotten through the statistical software used.

Sample size = 5

Correlation coefficient = -9.09

In conclusion, the coefficient is -9.09.

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Probability of (a) George winning is 0.1

                       (b) Julia winning is 0.05

Given in question,

Total ticket sold = 100

George bought tickets = 10

Julia bought tickets = 5

Winning ticket = 1

Selecting 1 ticket from 100 = [tex]\left[\begin{array}{ccc}100\\1\\\end{array}\right][/tex]

                                            = 100

Selecting 1 ticket from 10 = [tex]\left[\begin{array}{ccc}10\\1\\\end{array}\right][/tex]

                                         = 10

Selecting 1 ticket from 5 = [tex]\left[\begin{array}{ccc}5\\1\\\end{array}\right][/tex]

                                        = 5

Probability = favorable outcome/total outcome

Probability of George winning = [tex]\frac{10}{100}[/tex]

                                                  = 0.1

Probability of Julia winning = [tex]\frac{5}{100}[/tex]

                                             = 0.05

Hence, probabilities are 0.1 and 0.05 respectively.

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The equations y = -6x² + 1 and y = 3x² + 4 both have graphs that are wider than the graph of y = 5x² - 3.To determine which equation has a graph wider than the graph of y = 5x² - 3, we need to compare the coefficients of x² in each equation.

A wider graph indicates a smaller coefficient in front of x², which means the parabola will be less steep and have a broader shape.Let's compare the coefficients:y = 8x² - 10: The coefficient is 8, which is larger than 5. Therefore, this equation does not have a wider graph than y = 5x² - 3.

y = 5x² + 2: The coefficient is 5, which is equal to the coefficient in y = 5x² - 3. Therefore, the graphs of these two equations will have the same width.

y = -6x² + 1: The coefficient is -6, which is smaller than 5. Hence, this equation has a wider graph than y = 5x² - 3.

y = 3x² + 4: The coefficient is 3, which is smaller than 5. Hence, this equation also has a wider graph than y = 5x² - 3.

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The x value we get is 10 when the sides are 8x-13 and 5x+17 in a congruent triangle.

Given that,

The sides as 8x-13 and 5x+17

We have to find the x value.

If two or more triangles are congruent, it depends on how big their sides and angles are. The three sides and three angles of a triangle determine its size and shape, accordingly. Two triangles are said to be congruent if the pairings of respective sides and corresponding angles are equal.

We say now,

8x-13 = 5x+17

8x-5x=17+13

3x=30

x=30/3

x=10

Therefore, The x value we get is 10 when the sides are 8x-13 and 5x+17 in a congruent triangle.

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Answer:

3

Step-by-step explanation:

f(1)=2(1)+1

f(1)=3

The exact arc length of f(x)=√2x+1 is 4.5.

The arc length is the separation between two points along a curve segment. The arc length of a function f(x) is given by the formula,

[tex]L=\int\limits^a_b {\sqrt{1+f'(x)^2}} \, dx[/tex]

Where f'(x) is derivative of function f(x). The arc length is, to put it simply, the distance that passes across the curved line of the circle that forms the arc. It should be noted that the arc's length is greater than the separation of its ends along a straight line.

Finding the arc length of f(x)=√2x+1 0≤x≤4, using the formula,

First finding the derivative of function,

[tex]f'(x)=\frac{d(\sqrt{2x+1})}{dx} \\\\=\frac{2}{2\sqrt{2x+1}} \\\\=\frac{1}{\sqrt{2x+1}}[/tex]

Now, putting the derivative of function f(x) in the formula of arc length L,

[tex]L=\int\limits^a_b {\sqrt{1+f'(x)^2}} \, dx\\\\L=\int\limits^4_0 {\sqrt{1+(\frac{1}{\sqrt{2x+1}})^2}} \, dx\\\\L=\int\limits^4_0 {\sqrt{1+\frac{1}{2x+1}}}\\\\L=\int\limits^4_0 {\sqrt{\frac{2x+1+1}{2x+1}}}\\L=\int\limits^4_0 {\sqrt{\frac{1}{2x+1}}}\\\approx4.5[/tex]

Therefore, the exact arc length of f(x)=√2x+1 is 4.5.

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The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;

⇒ y = - 4°x + 0°

What is an expression?

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

Given that;

At 2 hours before sunset, the temperature is 0°F.

And,  At 2 hours after sunset, the temperature is −4°F.

Now,

Let the temperature in degrees Fahrenheit = y

So, We can formulate;

⇒ y = - 4°x + 0°

Thus, The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;

⇒ y = - 4°x + 0°

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Distance is the total length covered by an object.

Displacement is the distance between the final point and the initial point.

The distance of the helicopter's flight is 150 m

The displacement of the helicopter's flight is zero.

Displacement is the distance between the final point and the initial point.

We have,

A helicopter lifts 75m vertically into the air and then comes back down to the ground.

Distance is the total length covered by an object.

Distance of the helicopter's flight.

= 75m + 75m

= 150 m

Displacement of the helicopter's flight.

= Final point - Initial point

= 0 - 0

= 0  

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Answer:

to find the answer you just need to divide 3 out of 141

141÷3=47seeds per each student

3x=141

x=141÷3

x=47

The equation is represented as A = S/3 , where S is the total number of seeds and A is the number of seeds planted by each student and the value of A = 47 seeds

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total number of seeds by each student be A

Now , the equation will be

The total number of seeds be S = 141 seeds

The number of students be n = 3 students

So , the total number of seeds planted by each student A = total number of seeds S / number of students n

A = S / n

Substituting the values in the equation , we get

Total number of seeds planted by each student A = 141 / 3

Total number of seeds planted by each student A = 47 seeds

Therefore , the value of A is 47 seeds

Hence , the number of seeds is 47 seeds

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