A rectangular prism has a length of 7 cm, a width of 4 cm, and a height of 2 1/2cm.

The prism is filled with cubes that have edge lengths of 1/2 cm.



How many cubes are needed to fill the rectangular prism?

Enter your answer in the box.

To fill the rectangular prism,
cubes are needed.

The balance after 5 years, if $1500 is deposited in an account with 6%

interest rate, compounded continuously is calculated as: $2,024.79.

The formula for calculating the balance (F) in a continuously compounded account is:

[tex]F = Pe^{(rt)}[/tex]

where we have:

P is the principal amount,

e is the mathematical constant approximately equal to 2.71828, and

r is the interest rate, and t is the time in years.

In this case, P = $1500, r = 6%, and t = 5 years.

Plug these values into the formula and solve for F:

F = 1500e^(0.065)

F = 1500e^0.3

F = 15001.34985880758

F = $2,024.79 (rounded to the nearest cent)

Therefore, the balance after 5 years is $2,024.79.

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The equations that can be used to solve for y, the length of the room are y * (y - 5) = 750, y^2 - 5y = 750 and (y + 25)(y – 30) = 0

From the question, we have the following parameters that can be used in our computation:

Area = 750

Length = y

Width = y - 5

The area is the product of the length and the width

So, we have

y * (y - 5) = 750

When expanded. we have

y^2 - 5y = 750

Lastly, we have

(y + 25)(y – 30) = 0 -- when factored

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12π inches is the circumference of the given circle with a diameter of 12 inches.

The circumference of a circle can be found using the formula C = π*d, where d is the diameter of the circle.

If the diameter of the circle is 12 inches, then the circumference is:

C = π* d

C = π * 12 inches

C = 12π inches

So, the circumference of the circle in terms of π is 12π inches.

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The concept Pythagoras theorem is used here to determine the length of the hypotenuse. It is an important theorem which explains the relation between the sides of a right angled triangle. The length of hypotenuse is

According to Pythagoras theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides. The sides of this triangle have been named perpendicular base and hypotenuse.

Hypotenuse² = Perpendicular² + Base²

9² + 4² = 97

√97 = 9.84 cm

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Your question is incomplete most probably your full question was:

What is the length of the hypotenuse of the triangle when x=9 now and other side y = 4.

Answer:

  u = -4

Step-by-step explanation:

You want the solution to the equation 16u -5u +18 = 3u -14.

The equation can be simplified by combining like terms:

  11u +18 = 3u -14

Adding (-18-3u) to both sides, we have ...

  8u = -32

  u = -32/8 = -4 . . . . . . divide by the coefficient of u

The solution is u = -4.

Using function notation on the table, we can say that:

f(3) = -2

When f(x) = -5, x = 4

Function notation is defined as a way of expressing a relationship between two variables.

From the given table, we see that:

when x = -6, f(x) = 8

when x = 7, f(x) = 3

when x = 4, f(x) = -5

when x = 3, f(x) = -2

when x = -5, f(x) = 12

Thus, we can say that:

f(3) = -2

When f(x) = -5, x = 4

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Answer:

36cm

Step-by-step explanation:

The lightning bolt on the right is 3 times bigger than the one on the left. You can tell this because that leftside, vertical-ish piece (on both of them) is labelled. The small one is 25cm and the big one is 75cm.

25 × 3 = 75

The bottom right side is 12cm, so times by 3 to find the bigger one that matches.

12 × 3 = 36

92 more students favor visiting Florida than Colorado

From the question, we have the following parameters that can be used in our computation:

Students = 400

Florida = 38%

Colorado = 15%

The percentage difference is

Difference = 38% - 15%

So, we have

Difference = 23%

This means that

Students = 23% * 400

Evaluate

Students = 92

Hence, the number of students is 92

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The triangles are classified according to their sides as:

1. equilateral 2. Scalene   3. and 4. Isosceles   5. equilateral     6. and 7. scalene triangle.      8. Isosceles   9. and 10. Equilateral

Recall the following:

A triangle is equilateral if all three sides are equal.

It is isosceles if it has two equal sides.

A triangle is scalene if all three sides are of different lengths.

1. The triangle is equilateral because all sides are equal.

2. Scalene

3. and 4. Isosceles (two sides are equal)

5. All sides are equal, so it is an equilateral triangle.

6. and 7. The three sides have different lengths, therefore, it is a scalene triangle.

8. Isosceles

9. and 10. Equilateral

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Check the picture below.

Answer: Angle one equals -15, and angle two equals 14, if the +7 equals a positive seven.

Step-by-step explanation:

There are more negatives than positives, so we make the ending answer negative, giving us -15. And the second one is simple multiplication, you double the 7 times two, or vice versa.

Hope this helps!

The largest interior angle of the triangle is the angle A

The side lengths of the triangles are given as

b = 10 cm

a = 14 cm

The other side length is not given

So, we solve the question using the two side lengths

Having said that:

The general rule is that; the higher the side length, the larger the angle

14 cm is greater than 10 cm

This means that the angle A is greater than the angle B

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The degree and the independent term of each of the following polynomials include the following;

Degree of P(x) is 4.

Independent term of P(x) is 7.

Degree of Q(x) is 3

Independent term of Q(x) is 1.

In Mathematics, a polynomial function simply refers to a type of mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.

Generally speaking, the degree of a polynomial function is sometimes referred to as an absolute degree and it is the greatest exponent (leading coefficient) of each of its term.

Additionally, the independent term is a number that isn't accompanied by any variable i.e it is a constant.

P(x) = 2x⁴ - 2x³ - 3x² + 7; degree = 4 and independent term = 7.

Q(x) = -x³ + 5x²-3x + 1; degree = 3 and independent term = 1.

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Complete Question:

Write the degree and the independent term of each of the following polynomials.

Breanna and Qasim must contribute $22,583.39 per year for eight years to have enough money to pay for their daughter's university education.

To determine the yearly contribution required for Breanna and Qasim, we need to use the present value formula for an annuity.

The formula is:

PV = C * ((1 - (1 + r)⁻ⁿ) / r)

Where PV is the present value of the annuity, C is the annual contribution, r is the annual interest rate, and n is the number of years.

First, we need to calculate the present value of the contributions that Breanna and Qasim make for the first eight years. We can use the formula:

PV = C * ((1 - (1 + r)⁻ⁿ) / r)

Where C is the annual contribution, r is the annual interest rate, n is the number of years, and PV is the present value of the contributions.

We know that the annual contribution is the same for each of the eight years, so we can simplify the formula to:

PV = C * (((1 - (1 + r)⁻ⁿ) / r))

The present value of the contributions is equal to the future value of the withdrawals five years after the last contribution. We can use the future value formula for an annuity to calculate this:

FV = R * ((1 + r)ⁿ - 1) / r

Where FV is the future value, R is the annual withdrawal, r is the annual interest rate, and n is the number of years.

We know that the future value of the withdrawals is $51,100 per year, the interest rate is 4%, and the number of years is 5.

FV = 51,100 * ((1 + 0.04)⁵ - 1) / 0.04 = $246,387.19

This is the present value of the contributions that Breanna and Qasim make over the first eight years. We can now solve for the annual contribution required using the present value formula:

PV = C * (((1 - (1 + r)⁻ⁿ) / r))

$246,387.19 = C * (((1 - (1 + 0.04)⁻⁸) / 0.04))

C = $22,583.39

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The amount of money that will be in the account after 10 years is: $1297.70

The formula for solving compound interest is expressed as:

A = P(1 + r/n)^(nt)

where:

A is Accrued amount (equal to principal added to interest)

P is the Principal amount

r is the annual nominal interest rate expressed as a decimal

R is termed as the annual nominal interest rate which is expressed as a percentage

r is equal to R/100

n is the number of the compounding periods per unit of the time

t is the time which is expressed in decimal years

We are given:

r = 0.0375

n = 2 times per year

t = 10 years

P = $895

Thus:

A = 895(1 + 0.0375/2)^(2 * 10)

A = $1297.70

Thus, that is the money that will be in the account after a period of 10 years

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Answer:

If the shoes are 20% off, then the sale price of the shoes will be:

67 - 0.20 * 67 = 67 - 13.40 = 53.60

So the sale price of the shoes is $53.60.

If the sales tax is 5%, then the tax on the shoes will be:

0.05 * 53.60 = 2.68

So the tax on the shoes is $2.68.

To find the total price of the shoes including tax, we need to add the sale price of the shoes and the tax:

53.60 + 2.68 = 56.28

Therefore, the total price of the shoes, including tax, is $56.28.

Answer:

$56.28

Step-by-step explanation:

1. Find the shoes' sale price.

The shoes are 20% off. We will find the new price by first finding 20% of $67.

An easy way to do it:

10% of 67 = 6.7
20% of 67 = 13.4

to double the percentage of the first equation, double the answer.

Now that we know 20% of 67 we can take away 20% from it:

67 - 13.4 =53.6

Money uses 2 decimal points so we will add a 0 at the end of the result.

The price of the shoes with only the sale is $53.60.

2. Add sales tax

First find out 5% of $53.60.

An easy way to do it:

10% of 53.60 = 5.360

5% of 53.60 = 2.68

to half the percentage of the first equation, half the answer.

Now that we know the price of the tax we can add it to our shoe price. With the sale the shoe costs $53.60 and we will add our tax:

53.60 + 2.68 = 56.28

Add your units:

Answer:

20%  (D)

Step-by-step explanation:

Part A: Note that the best graphical representation to use for this kind of data is a Histogram.

Part B : Creating the historgram means you have to first chose the intervals for the data.

When it comes to displaying the distribution of a set of continuous data, histograms offer an appropriate visualization method.

This display type divides the data into intervals and plots the number of observations that fall within each interval, hence providing frequency distribution information.

For instance, in creating a histogram for this particular dataset, one can choose intervals or bins with sizes e.g. 5 units covering a range between 0 and 30 before tabulating the count of observed variables in each bin and plotting these counts on the chart's vertical axis.

A histogram illustrates how often students ate breakfast within a 30-day timeframe. This frequency distribution features labeled axes, with the vertical axis representing "Frequency" and the horizontal axis depicting "Number of times students ate breakfast."

Each bar on the horizontal axis corresponds to an interval and shows its frequency on a scaled height basis.

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Answer:

The function f(x,y) = x^2 + y^2 represents the equation of a paraboloid with its vertex at the origin. Since the function increases as we move away from the origin, there are no maximum points, but there is a minimum point at the origin.

To find this minimum point, we can take the partial derivatives of f(x,y) with respect to x and y, and set them equal to zero:

df/dx = 2x = 0

df/dy = 2y = 0

Solving these equations simultaneously gives us x = 0 and y = 0, which is the only critical point of the function. To determine whether this point is a minimum or maximum, we can use the second partial derivative test.

Taking the second partial derivatives, we have:

d^2f/dx^2 = 2

d^2f/dy^2 = 2

d^2f/dxdy = 0

At the point (0,0), both second partial derivatives are positive, which indicates that the point is a minimum. Therefore, the function f(x,y) = x^2 + y^2 has a minimum value of 0 at the point (0,0).

The height of the rectangle is approximately 15.5 inches.

Let's call the height of the rectangle "h". We know that the width is 47 inches longer than the height, so the width can be expressed as "h + 47".

We can use the Pythagorean theorem to solve for the height. The Pythagorean theorem states that for a right triangle with legs of length "a" and "b" and hypotenuse of length "c", a^2 + b^2 = c^2.

In this case, we can consider the rectangle to be a right triangle, with the height as one leg, the width as the other leg, and the diagonal as the hypotenuse. So we can write:

h^2 + (h + 47)^2 = 65^2

Simplifying this equation gives:

2h^2 + 94h - 1476 = 0

We can solve for "h" using the quadratic formula:

h = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 2, b = 94, and c = -1476. Plugging these values into the quadratic formula gives:

h = (-94 ± sqrt(94^2 - 4(2)(-1476))) / 4

Simplifying this expression gives:

h = (-94 ± sqrt(10084)) / 4

h = (-94 ± 100.42) / 4

h = -48.6 or 15.42

Since the height of the rectangle cannot be negative, we can discard the negative solution. Therefore, the height of the rectangle is approximately 15.5 inches.

The ordered pairs to a solution for the given linear equation are (-1, 3.5) and (4, -4).

To find the ordered pair that is a solution to the equation 6x + 4y = 8, we can substitute the given value of x or y and solve for the other variable.

For the first option, substituting x = -1, we get:

6(-1) + 4y = 8

-6 + 4y = 8

4y = 14

y = 3.5

So, the ordered pair (-1, 3.5) is a solution to the equation.

For the second option, substituting y = -4, we get:

6x + 4(-4) = 8

6x - 16 = 8

6x = 24

x = 4

So, the ordered pair (4, -4) is a solution to the equation.

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Answer:

A parallelogram is a quadrilateral with 2 pairs of parallel sides.

Step-by-step explanation:

Mark brainliest, pls

The equation of the line perpendicular to y=1/2x-1 and passing through the point (5,6) is y = -2x + 16.

To find the equation of the line perpendicular to y=1/2x-1, we need to determine its slope. We can recall that the slope of a line in slope-intercept form, y = mx + b, is given by m, the coefficient of x. So in the given equation y=1/2x-1, the slope is 1/2.

The slope of a line perpendicular to this line will be the negative reciprocal of the slope, which means it will be -2. To see why this is true, remember that the product of the slopes of two perpendicular lines is always -1. So if the slope of the original line is m, the slope of the perpendicular line will be -1/m.

Now that we know the slope of the perpendicular line is -2, we can use the point-slope form of the equation of a line to find its equation. The point-slope form is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

We are given a point on the perpendicular line, (5, 6), so we can substitute that into the equation and also substitute in the slope, -2:

y - 6 = -2(x - 5)

y - 6 = -2x + 10

y = -2x + 16

Hence, the equation of the line perpendicular to y=1/2x-1 and passing through the point (5,6) is y = -2x + 16.

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The graph of the system of inequalities is on the image at the end.

Here we have the system of inequalities:

y > -2x + 9

y < 5x - 6

First we need to graph both of these lines with dashed lines (that is because the values on top of the lines are not solutions for the inequalities).

Then we need to shade the region above the first line, and the region below the second line.

Thenh the graph of the system is the one you can see in the image at the end.

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The factorized form of the quadratic equation is:

4(x - 3)*(x + 0.25) = 0

The quadratic equation is 4x² - 11x -3 = 0

To do that, we need to find the zeros, so let's use the quadratic formula:

[tex]x = \frac{11 \pm \sqrt{(-11)^2 - 4*4*-3} }{2*4} \\\\x = \frac{11 \pm 13 }{8}[/tex]

Then the two roots are:

x = (11 + 13)/8 = 3

x = (11 - 13)/8 = -2/8 = -0.25

Then the factorized form is:

4(x - 3)*(x + 0.25) = 0

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Using the given information, the cost of Max's electricity bill is R551.10

From the question, we are to calculate the cost of Max's monthly electricity bill

From the given information,

"Max's monthly electricity budget only allows him to use 250.50 kWh"

and

"The cost for 1 kWh is R2.20"

To determine the cost of Max's monthly electricity bill, we will multiply his monthly electricity budget by the cost for 1 KWh

That is,

Max's monthly electricity bill = 250.50 × R2.20

Max's monthly electricity bill = R551.10

Hence,

The cost of Max's monthly electricity bill is R551.10

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Answer:2^4=4x-4 would be the answer

Step-by-step explanation: You would exponentiate both sides

The value of 5cos(tetha) + 4/sin(beta) is 9

Complementary angles are two angles that sum up to 90°. This means that in a right angled triangle sin( beta) is thesame as cos(90-tetha) and cos (beta) is sin(90-tetha).

Examples of complementary angles include: 30 and 60, 50 and 40 e.t.c

Therefore if tan ( tetha ) = 3/4, and tan(tetha) = opp/adj. This means opp is 3 and adj is 4

therefore hyp = √3²+4²

= √9+16 = √25

= 5

therefore cos(tetha) = 4/5

and sin beta = 4/5

therefore 5cos(tetha) + 4/sin(beta) = 5 × 4/5 +(4÷4/5)

= 4+5 = 9

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The numbers as an integer or not are:

From the question, we have the following parameters that can be used in our computation:

7/10 - yes or no

-6/1 - yes or no

-30.18 - yes or no

7 - yes or no

-76 - yes or no

integers are numbers without decimal point (including 0)

Using the above as a guide, we have the following:

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