A rectangular prism with a volume of 555 cubic units is filled with cubes with side lengths of \dfrac13
3
1
​
start fraction, 1, divided by, 3, end fraction unit.
How many \dfrac13
3
1
​
start fraction, 1, divided by, 3, end fraction unit cubes does it take to fill the prism?

Answer:

m = 0.75

Step-by-step explanation:

Since (m, 2m + 1 ) is a solution of the equation then substituting the values into the equation will make it true, that is

substitute x = m and y = 2m + 1 into the equation, thus

4m + 2(2m + 1) = 8 ← distribute and simplify left side

4m + 4m + 2 = 8

8m + 2 = 8 ( subtract 2 from both sides )

8m = 6 ( divide both sides by 8 )

m = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex] = 0.75

Answer:

y = 2x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{1}{2}[/tex] x - 4 ← is in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2, thus

y = 2x + c ← is the partial equation

To find c substitute (3, 3) into the partial equation

3 = 6 + c ⇒ c = 3 - 6 = - 3

y = 2x - 3 ← equation of perpendicular line

The equation of the line passing through (3, 3) and perpendicular to y = -1/2x - 4, is y = 2x - 3.

To find the equation of a straight line passing through the point (3, 3) which is perpendicular to the line y = -1/2x - 4, follow these steps:

Therefore, the equation of the line passing through the point (3, 3) and perpendicular to the line y = -1/2x - 4 is y = 2x - 3.

Answer:

6

Step-by-step explanation:

(-1)^2=(-1)(-1)=1

2(1)(3)=2*3=6

2x*2y

Replace x with -1 and y with 3

2(-1) * 2(3)

2*-1 = -2

2*3=6

Now multiply -2 with 6 and it should be -12.

Answer:

Velocity equation

[tex]v=\frac{d}{t}[/tex]

Step-by-step explanation:

Given:

Velocity of the car v = 4 units

and time t = 2 seconds

Let d = distance

Find the velocity equation.

The equation of the velocity is given below.

[tex]velocity=\frac{distance\ travelted}{time\ to\ distance\ travel}\ unit/sec[/tex]

[tex]v=\frac{d}{t}[/tex]

The above equation says, the distance travelled in t times is called velocity.

The unknown value in given question is distance. so, we find distance by given value.

[tex]d = v\times t[/tex]

[tex]d = 4\times 2[/tex]

[tex]d = 8\ units[/tex]

Therefore, the distance travelled by car is 8 units.

Formula for velocity: V = d/t

V = velocity

d = distance

t = time traveled

We are given the variables t = 2 and v = 2.

Substitute these values into the formula.

4 = d/2

Solve for d (d = distance).

4 = d/2

4 * 2 = d/2 * 2

8 = d

Therefore, the car traveled a distance of 8 units.

Best of Luck!

Answer: 3/15 or 1/5

Step-by-step explanation:

Each person will get 1/15 of each watermelon so 3/15 of watermelon that can be simplified to 1/5

Final answer:

Each of the fifteen friends will receive ⅔ of a watermelon when 3 watermelons are shared equally among them.

Explanation:

If fifteen friends want to share 3 watermelons equally, we need to divide the total number of watermelons by the number of friends to find out what fraction of a watermelon each friend will get.

To find the answer, you start with 3 watermelons and divide them by 15 friends, which is:

3 watermelons ÷ 15 friends = ⅔ of a watermelon per friend.

Thus, each friend will get ⅔ of a watermelon.

If an average person listens to music for 1,000 hours in a year, the probability that the component lasts for more than 3 years is 2.3%.

In Mathematics and Statistics, the z-score of a given sample size or data set can be calculated by using the following formula:

Z-score, z = (x - μ)/σ

Where:

σ represents the standard deviation.

x represents the sample score.

μ represents the mean score.

Since an average person listens to music for 1,000 hours in a year, the total life span of the component for 3 years can be calculated as follows;

Total life span = 3 × 1000

Total life span = 3000 years.

By substituting the parameters into the z-score formula, we have the following:

Z-score, z = (3000 - 2400)/300

Z-score, z = 2.0

Based on the standardized normal distribution table, the required probability is given by:

P(X > 3000) = P(x > Z)

P(X > 3000) = 1 - P(Z < 2)

P(X > 3000) = 1 - 0.9773

Probability = 0.0227 × 100.

Probability = 2.27 ≈ 2.3%.

43.326 megabytes has been downloaded

Solution:

Given that a file that is 261 megabytes is being downloaded

16.6 % of download is complete

To find: megabytes that have been downloaded

From given question,

16.6 % of 261 megabytes has been downloaded

Let us find 16.6 % of 261

We know that,

a % of b can be written in fraction as [tex]\frac{a}{100} \times b[/tex]

So 16.6 % of 261 is calculated as:

[tex]16.6 \% \text{ of }261 = 16.6 \% \times 261\\\\\rightarrow \frac{16.6}{100} \times 261\\\\\rightarrow 0.166 \times 261\\\\\rightarrow 43.326[/tex]

Thus 43.326 megabytes has been downloaded

Answer:

[tex]y=-4x+5[/tex]

Step-by-step explanation:

Step 1:  Find the slope

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{13-5}{-2-0}[/tex]

[tex]m=-\frac{8}{2}[/tex]

[tex]m=-4[/tex]

Step 2:  Use point slope form

[tex](y-5) = -4(x-0)[/tex]

[tex]y-5 + 5=-4x + 5[/tex]

[tex]y=-4x+5[/tex]

Answer:  [tex]y=-4x+5[/tex]

y=-4x+5

Step-by-step explanation:

Step 1:  Find the slope

m=\frac{y_2-y_1}{x_2-x_1}

m=\frac{13-5}{-2-0}

m=-\frac{8}{2}

m=-4

Step 2:  Use point slope form

(y-5) = -4(x-0)

y-5 + 5=-4x + 5

y=-4x+5

Answer:390 miles

Step-by-step explanation:

speed*time=distance (keep that in mind)

8 2/3 is also equal to 26/3

take that number and multiply that by 45 min

45*26/3

that equall 390 miles

(I tried my best, I might be wrong)

Answer:

13/2

Step-by-step explanation:

Keep in mind that speed*time=distance

ok so, if you convert 8 2/3 in to a improper fraction you'll get 26/3. Now we have to turn 45 minutes into a fraction so it's easier to multiply, that would be 45/60 because 1 hour has 60 minutes. Now, we would multiply 26/3 and 45/60 and get 78/12. Simplify that and get 13/2

Answer: 31

Step-by-step explanation: A coefficient is a number that appears in front of a variable. So in this case, since 31 appears in front of the variable y, 31 is the coefficient.

Now, you might think that 7 is a coefficient also but it's not. The reason it's not is because it doesn't have a variable attached to it so a coefficient needs to have a variable next to it.

Answer:

13 trails

Step-by-step explanation:

The histogram shows following numbers of trails:

So, there are 5 trails with length less than 6 km and 4 + 1 + 3 = 8 trails that are at least 24 km long.

In total, 5 + 8 = 13 trails

Answer:

[tex]y-2=-5(x - 2)[/tex]

Step-by-step explanation:

Given:

The equations given are:

[tex]y-2=-5(x - 2)\\X+ 7 = -4(X + 8)\\y - 3 = y(x + 4)\\y + 9 = x(x - 1)[/tex]

Now, a linear function is of the form:

[tex]y=mx+b[/tex]

Where, 'm' and 'b' are real numbers and [tex]m\ne0[/tex]

Equation 1: [tex]y-2=-5(x - 2)[/tex]

Simplifying using distributive property, we get:

[tex]y-2=-5x+10\\y=-5x+10+2\\y=-5x+12[/tex]

The above equation is of the form [tex]y=mx+b[/tex]. So, it represents a linear function.

Equation 2: [tex]X+ 7 = -4(X + 8)[/tex]

Here, both sides of the equation has same variable 'X'. So, it will form an equation of 1 variable. So, it's not a linear function.

Equation 3: [tex]y - 3 = y(x + 4)[/tex]

Simplifying the above equation. This gives,

[tex]y-3=yx+4y\\y-4y-yx=3\\y(1-4-x)=3\\y(-3-x)=3\\y=\frac{3}{(-3-x)}[/tex]

This is not of the form of the linear function. So, it is also not a linear function.

Equation 4: [tex]y + 9 = x(x - 1)[/tex]

Simplifying the above equation. This gives,

[tex]y+9=x^2-x\\y=x^2-x-9[/tex]

This is not of the form of the linear function. So, it is also not a linear function.

Answer:

A

Step-by-step explanation:

on edge 2020

Answer:

y+1=2(x+3)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-1)=2(x-(-3))

y+1=2(x+3)

Answer:

7/10

Step-by-step explanation:

3/10+2/5=3/10+4/10=7/10

Answer: 7/10

Step-by-step explanation: To add these two fractions together, we start by finding their common denominator.

The common denominator for 10 and 5 will be the least common multiple of 10 and 5 which is 10.

Since 10 already has a 10 in the denominator, it stays the same.

We multiply top and bottom of our second fraction by 2 and we get 4/10.

Now we are adding like fractions so we simply add across the numerators and keep the same denominator.

So, 3/10 + 4/10 = 7/10.

Therefore, 3/10 + 2/5 = 7/10.

Answer:

Step-by-step explanation:

The percentage is 59 percent males 41 percent females

Answer: 12/13

Step-by-step explanation:

In a deck of cards there are 4 of each number. Therefore there are 4 sevens in the deck. 4/52 are 7, but you want the probability of getting a card that IS NOT 7. That means there are 48 cards that aren’t a 7. 48/52 is the probability. But you can simplify this by finding a number that divides evenly into both, which in this case is 4. This simplifies to 12/13.

Answer:

The total area of Tony's vegetable garden is 124 square feet

Step-by-step explanation:

The total area of Tony's vegetable garden is composed by three rectangles.

1st rectangle

Length = 10 feet

Width = 6 feet (14 - 8)

Area = 6 * 10 = 60 square feet

2nd and 3rd rectangles are equals

Length = 4 feet

Width = 8 feet (14 - 6)

Area = 2 * 4 * 8 = 2 * 32 = 64 square feet

Total area

Area of the three rectangles

60 + 64 = 124 square feet

The total area of the vegetable garden is 124 ft.

A rectangle is a quadrilateral in which opposite sides are parallel and congruent to each other.

The area of a rectangle is the product of its length and width. It is given by:

Area = length * width

Area of the vegetable garden = (8 ft * 4 ft) + (8 ft * 4 ft) + (10 ft * (14 - 8)ft)

Area of the vegetable garden = 32 ft + 32 ft + 60 ft = 124 ft.

Therefore the total area of the vegetable garden is 124 ft.

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Answer:

265 Fahrenheit.

Step-by-step explanation:

It is given that,

Highest temperature ever recorded on earth = 136 Fahrenheit

Lowest temperature = -129 Fahrenheit

We need to plot these temperature as an integer on a number line.

136 is a positive integer. So, it lies 136 units on the right side of zero.

-129 is a negative integer. So, it lies 129 units on the left side of zero.

According to absolute values, |x|=|-x|=x.

Absolute value of 136 and -129 are

[tex]|136|=136[/tex]

[tex]|-129|=129[/tex]

The difference between he two temperatures is

[tex]|136-(-129)|=|136+129|=265[/tex]

Therefore, the difference between he two temperatures is 265 Fahrenheit .

The question focuses on Mathematics, specifically Geometry and Calculus. It requires calculating the area of geometric figures especially circles and disks in terms of π, often via the formula A=πr² or integration.

From the question, we are required to find the area of shaded parts, which essentially associates with geometric figures and their properties in Mathematics. Specifically, this question appears to focus on areas related to circles and spheres, as it mentions calculations in terms of π, radius (r) and certain formulas like A=πr², which is the formula for the area of a circle.

When asked to express something in terms of π, it typically means leaving the answer as multiples of π, rather than using its decimal equivalent. So for instance, if we calculated the area of a circle with a radius of 3 using A=πr², we would say that the area is 9π.

Another crucial information that surfaced in the materials provided is the area calculation using integration, which involves adding up the individual areas of 'thin rings' from r=0 to r=R where R is the total radius of the disk or circle. This is an important aspect of finding areas under curves or finding areas enclosed by curves in Calculus.

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The area of the shaded regions is [tex]\(8\pi - 8\)[/tex] square centimeters.

To find the area of the shaded regions in the circle with the inscribed triangle, we'll follow these steps:

1. Calculate the Area of Sector AOC:

  - The sector's central angle is 90° because triangle AOC is right-angled at C.

  - The area of a sector is [tex]\( \frac{\theta}{360} \times \pi \times r^2 \)[/tex], where [tex]\( \theta \)[/tex] is the central angle and [tex]\( r \)[/tex] is the radius.

  - Here, [tex]\( r = 4 \) cm and \( \theta = 90° \).[/tex]

  - So, the area of sector AOC is [tex]\( \frac{90}{360} \times \pi \times 4^2 = \pi \times 4 \) cm^2.[/tex]

2. Calculate the Area of Triangle AOC:

  - The area of a triangle is [tex]\( \frac{1}{2} \times \text{base} \times \text{height} \).[/tex]

  - For triangle AOC, the base and height are both equal to the radius, which is 4 cm.

  - So, the area of triangle AOC is [tex]\( \frac{1}{2} \times 4 \times 4 = 8 \)[/tex] cm².

3. Calculate the Area of the Shaded Segment on the Opposite Side:

  - Subtract the area of triangle AOC from the area of sector AOC.

  - This gives us the area of the shaded segment: [tex]\( \pi \times 4 - 8 \)[/tex] cm².

Combining both shaded areas, the total area of the shaded regions is [tex]\( \pi \times 4 + (\pi \times 4 - 8) \)[/tex] cm², which simplifies to [tex]\( 8\pi - 8 \)[/tex] cm². Therefore, the area of the shaded regions is [tex]\( 8\pi - 8 \)[/tex] cm².

Answer:  The required x-co-ordinate of the point of intersection of two lines is [tex]-\dfrac{2bm}{m^2+1}.[/tex]

Step-by-step explanation:  Given that two perpendicular lines have opposite y-intercept and the equation of one of the lines is

[tex]y=mx+b.[/tex]

We are to express the x-coordinate of the intersection point of the lines in terms of m and b.

Let the slope and y-intercept of the other line be s and c respectively.

Since the product of the slopes of two perpendicular lines is -1 and -b is the opposite of b, so we have

[tex]ms=-1~~~\Rightarrow s=-\dfrac{1}{m}[/tex]

and c = -b.

That is, the equation of the other line is

[tex]y=sx+c\\\\\Rightarrow y=-\dfrac{1}{m}-b.[/tex]

Comparing the equations of both the lines, we get

[tex]mx+b=-\dfrac{1}{m}x-b\\\\\\\Rightarrow mx+\dfrac{1}{m}x=-2b\\\\\\\Rightarrow \dfrac{m^2+1}{m}x=-2b\\\\\\\Rightarrow x=-\dfrac{2bm}{m^2+1}.[/tex]

Thus, the required x-co-ordinate of the point of intersection of two lines is [tex]-\dfrac{2bm}{m^2+1}.[/tex]

Final answer:

The x-coordinate of the intersection point for two perpendicular lines with opposite y-intercepts can be expressed as x = -2b/(m + 1/m), where m is the slope and b is the y-intercept of one of the lines.

Explanation:

When we have two perpendicular lines with opposite y-intercepts, and one of the lines has the equation y = mx + b, we can find the x-coordinate of the intersection point by expressing the other line's equation.

Since the other line is perpendicular, its slope will be the negative reciprocal of m. Therefore, if the first line's slope is m, the second line's slope will be -1/m. Also, if the y-intercept of the first line is b, the y-intercept of the second line will be -b, given that they are opposite.

The equation of the second line will then be y = (-1/m)x - b. To find the intersection point, we set the y-values of both equations equal to each other:

mx + b = (-1/m)x - b

Now, let's solve for x:

mx + (1/m)x = -2b

x(m + 1/m) = -2b

x = -2b/(m + 1/m)

Thus, the x-coordinate of the intersection point in terms of m and b is x = -2b/(m + 1/m).

Answer:

x=-19/3

Step-by-step explanation:

(3x-1)/4=-5

3x-1=-5*4

3x-1=-20

3x=-20+1

3x=-19

x=-19/3

Answer:

Step-by-step explanation:

3x-1/4=-5

3x-0.25=-5

3x=-5.25

x=-1.75

The 24th term is 152

Step-by-step explanation:

The formula of the nth term of an arithmetic sequence is:

[tex]a_n=a+(n-1)d[/tex] , where

The third term means n = 3

∵ [tex]a_3=a+(3-1)d[/tex]

∴ [tex]a_3=a+2d[/tex]

∵ [tex]a_3[/tex] = 5

- Equate the right hand sides of the third term

∴ a + 2d = 5 ⇒ (1)

The fifth term means n = 5

∵ [tex]a_5=a+(5-1)d[/tex]

∴ [tex]a_5=a+4d[/tex]

∵ [tex]a_5[/tex] = 19

- Equate the right hand sides of the fifth term

∴ a + 4d = 19 ⇒ (2)

Now we have a system of equations to solve it

Subtract equation (1) from equation (2) to eliminate a

∴ 2d = 14

- Divide both sides by 2

∴ d = 7

- Substitute the value of d in equation (1) to find a

∵ a + 2(7) = 5

∴ a + 14 = 5

- Subtract 14 from both sides

∴ a = -9

The twenty fourth term means n = 24

∵ a = -9 and d = 7

- Substitute the values of a and d in the formula of the nth term

∴ [tex]a_24=-9+(24-1)(7)[/tex]

∴ [tex]a_24=-9+(23)(7)[/tex]

∴ [tex]a_24=-9+161[/tex]

∴ [tex]a_24=152[/tex]

The 24th term is 152

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Answer:

The answer is A I just too the test

Step-by-step explanation:

Answer:

A) 0.15

Step-by-step explanation:

Because 15/20=3/4=75/100=75%=0.75.

The other angles in the isosceles triangle with an angle of 100° will be 40°

Step-by-step explanation:

Lets define an isosceles triangle first.

"An isosceles triangle is a triangle with two equal sides and two equal angles.

Given that an angle of the triangle is 100°

We know that the sum of internal angles of a triangle is 180°

The sum of remaining two angles is:

=180°-100°

=80°

As the triangle is an isosceles triangle, the two angles will be equal.

So the angles will be:

[tex]=\frac{80}{2}\\=40[/tex]

The other angles in the isosceles triangle with an angle of 100° will be 40°

Keywords: Triangle, isosceles triangle

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9514 1404 393

Answer:

  3x +y = 2

Step-by-step explanation:

Standard form is ...

  ax +by = c

where a, b, c are mutually prime integers and the leading coefficient is positive.

We can put the equation in this form by adding 3x to both sides.

  y = -3x +2

  3x +y = 2 . . . . . add 3x to both sides. This is standard form.

Answer:

Step-by-step explanation:

If we are looking for the composition of f(g(7)), we will start at the innermost part of the problem, which is to evaluate g(7).  That means that we put 7 in for x in the g function and come up with a solution to that first.

If g(x) = x - 3, then g(7) = 7 - 3 which is 4.  Now take that 4 and put it in for x in the f function:

f(4) = [tex](4)^2+4[/tex] which is 16 + 4 which is 20

Therefore, f(g(7)) = 20

Answer:

If we are looking for the composition of f(g(7)), we will start at the innermost part of the problem, which is to evaluate g(7).  That means that we put 7 in for x in the g function and come up with a solution to that first.

If g(x) = x - 3, then g(7) = 7 - 3 which is 4.  Now take that 4 and put it in for x in the f function:

f(4) =  which is 16 + 4 which is 20

Therefore, f(g(7)) = 20

Step-by-step explanation:

Exponential functions are something like y = 2^x where the variable is in the exponent (ie the exponent isnt a fixed number). What is given here, y = 3x^3, is a cubic function. You can also call this a power function. Power functions are of the form a*x^b, where a & b are constants.

Answer:

5x+y=6

Step-by-step explanation:

y=-5x+6

y-(-5x)=6

y+5x=6

5x+y=6

The equation in standard form can be written as; 5x+y=6

An equation is an expression that shows the relationship between two or more numbers and variables.

Suppose the considered polynomial is of only one variable. Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.

We have given the equation as;

y=-5x+6

Now,

y-(-5x)=6

y+5x=6

The equation in standard form can be written as;

5x+y=6

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The value of x is 58°

Step-by-step explanation:

we can see in the figure that the triangle formed is a right-angled triangle

In a right-angled triangle, one angle is always 90 degrees and the other two angles are complementary i.e. their sum is 90 degrees

So,

Using the axiom

[tex]32 + x = 90\\x = 90-32\\x = 58[/tex]

Hence,

The value of x is 58°

Keywords: Triangles, angles

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Answer:

3

Step-by-step explanation:

From the given indices

(3a^n)^3 X (1/3a^n)^3

We can rewrite the equation to be

(3a^n)^3 X (3a^-n) ^3

We father simplify;

3a^3n X 3a^-3n

Since we have same base, we add their relative powers, we solve thus,

3a^(3n-3n)

= 3a^0

= 3 X a^0 = 3 X 1

=1