What is the Volume of the prism below

Answer:

Step-by-step explanation:

To find the total distance traveled by the hikers to get home, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the straight line distance) is equal to the sum of the squares of the lengths of the other two sides.

Since the hikers traveled 3 km north and 4 km east, we can consider this as the sides of a right-angled triangle, with the hypotenuse being the straight line distance traveled to get home. So, the square of the distance traveled to get home is equal to the sum of the squares of the sides, i.e., 3^2 + 4^2 = 9 + 16 = 25. Taking the square root of 25 gives us 5 km, so the distance traveled by the hikers to get home is 5 km.

Answer:

$105

Step-by-step explanation:

Let x be the amount of money Carolina has in her checking account. Then, her savings account has x + $30. The total amount of money in both accounts is $180, so we can write the equation:

x + (x + $30) = $180

Expanding the left-hand side:

2x + $30 = $180

Subtracting $30 from both sides:

2x = $150

Dividing both sides by 2:

x = $75

Therefore, Carolina has $75 in her checking account and $75 + $30 = $105 in her savings account.

Answer:

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Let the number of pizzas be x.

The average cost per pizza is:

If we need the average cost be at most $3.50, we need an inequality:

This is translated as:

The blanks are:

Answer:

The service tax paid was:

0.06 * RM180 = RM10.80

Step-by-step explanation:

To calculate the service tax paid by Mr. Lim, we need to first find the amount of the bill before the service tax was added.

Let's call the original bill amount "x".

After the 6% service tax was added, the total bill became x + (0.06 * x) = RM190.80.

So we can set up the equation:

x + (0.06 * x) = RM190.80

Expanding the right side of the equation:

x + (0.06 * x) = 190.80

Combining like terms:

1.06x = 190.80

Solving for x:

x = 180

So the original bill amount before the service tax was added was RM180.

The service tax paid was:

0.06 * RM180 = RM10.80

You launch an object off a 55-foot cliff. If the object was launched at 85 feet/second,  64.23 feet/second long it will take for the object to hit the ground below. This can be solved using the concept of law of conservation of energy.

Three fundamental quantities all maintain their original values. Energy, momentum, and angular momentum are these. Energy is a conserved quantity, which could surprise you if you've read instances in previous pages, such the kinetic energy of charging elephants. The first law of thermodynamics, generally known as the law of conservation of energy, stipulates that the energy of a closed system must remain constant and cannot rise or fall on its own without external intervention.

Given that,

Height of the cliff, h= 55 Foot

Initial speed of the projectile, u = 85 m/s

Let, the projectile hit the ground with velocity "v"

Applying the law of conservation of energy,

mgh + 1/2 mu² = 1/2 mv²

or, m (gh + 1/2 u²) = 1/2 mv²

or, (gh + 1/2 u²) = 1/2 v²

or, 10 × 55 + (1/2 × (55)²) = 1/2 v²

or, 550 + 1512.5 = 1/2 v²

or, 2062.5 = 1/2 v²

or, 4125 = v²

or, v = 64.23 feet/second

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Answer:

Step-by-step explanation:

To find the probability of rolling a 6 on two number cubes, we need to calculate the number of favorable outcomes (rolling a 6 on either or both of the cubes) divided by the total number of possible outcomes.

Each cube has 6 sides, numbered 1 through 6. So, the total number of possible outcomes when rolling two cubes is 6 x 6 = 36.

The number of favorable outcomes is 2, because there are two ways to roll a 6: either rolling a 6 on the first cube and a 6 on the second cube, or rolling a 6 on one of the cubes.

So, the probability of rolling a 6 is:

favorable outcomes / total outcomes = 2 / 36 = 1/18

Therefore, the probability of rolling a 6 on two number cubes is 1/18 or approximately 5.56%.

3.1 The cash price of the NISSAN NP300 is R221,180 (incl. VAT).

3.2. it would take approximately 6.67 years to pay off the vehicle through instalments.

A deposit of approximately R22,282.70 would be needed if the financing plan requires a 10% deposit

3.1 The cash price of the NISSAN NP300 is R221,180 (incl. VAT).

3.2 The given information does not explicitly state the number of years for the instalment plan, but it does provide the number of months (80) and the total payment amount (R303,007). Assuming a monthly payment plan, we can calculate the number of years as follows:

Number of years = Number of months / 12

Number of years = 80 / 12

Number of years ≈ 6.67 years

So it would take approximately 6.67 years to pay off the vehicle through instalments.

To calculate the deposit needed, we need to subtract the residual amount from the total cash price. From the given information, the total payment is R303,007 and the residual is R80,180, so:

Cash price = Total payment - Residual

Cash price = R303,007 - R80,180

Cash price = R222,827

So the cash price is slightly higher than the advertised price of R221,180, likely due to financing fees or interest. To determine the deposit needed, we can assume a specific percentage of the cash price that must be paid upfront. For example, if the deposit required is 10% of the cash price, then:

Deposit = 0.1 x Cash price

Deposit = 0.1 x R222,827

Deposit = R22,282.70

So a deposit of approximately R22,282.70 would be needed if the financing plan requires a 10% deposit.

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The measure of <1 is 36 degree.

Complementary angles are those whose combined angle is exactly 90 degrees.

For example, 30 degrees and 60 degrees are complementary angles.

As, the complementary angle have sum of angles are 90 degree.

So, 2x+ 3x= 90

5x = 90

x= 18

Then, the measure of <CBD is 3x = 3(18)= 54 degree.

As, <1 is Complementary angle of <CBD.

So, the measure of <1 = 90- 54 = 36 degree

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Answer:

Step-by-step explanation:

The terms "4/10, 2/30, n/60" indicate that the buyer can take a discount of 4% if they pay within 10 days from the invoice date, or pay the full amount within 30 days from the invoice date. If the payment is made after 30 days, the buyer must pay the full amount plus any late fees that may apply.

Since the invoice was dated October 15 and the payment was sent on October 28, the payment was made within 30 days from the invoice date, so the buyer cannot take the 4% discount.

The total cost of 50 pairs of shoes at $85 per pair is 50 * 85 = $4250.

Therefore, the total amount of the check would be $4250, which is the full amount of the purchase price without the 4% discount.

Answer:

f(-7) = 15

Step-by-step explanation:

Subsitute x = - 7 into f (X) = - 3 (x+2)

f(-7) = -3 x (-7+2)

calculate the sum or difference

f(-7) =-3 x (-5)

determine the sign for multiplication or division

f(-7)=3x5

calculate the product or quotient

f(-7)=15

final awnser f(-7)=15

In the absence of trade between Glacier and Sequoia, Glacier would consume 8 million pairs of shorts and 48 million pounds of almonds, and Sequoia would consume 15 million pairs of shorts and 20 million pounds of almonds. However, if both countries decide to engage in trade, Glacier could specialize in producing shorts, using 1 million hours of labor per week, and Sequoia could specialize in producing almonds, using 1 million hours of labor per week. This specialization would result in Glacier producing 12 million pairs of shorts and Sequoia producing 24 million pounds of almonds. This would enable each country to consume more of both goods than they could produce in the absence of trade.

The relation is a function only if for element x in Set X, there is only one element in Set Y so, the choice B shows the relation.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable).

When a relation will be called as a function .

Consider there be a relation R from a set X to a set Y .

Since the relation will be called a function if each element of set X is related to exactly one element in set Y.

which is, an element x in X, there is only one element in Y that x is related to.

Therefore , the correct option is B.

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The lengths of the sides of the pentagon are;

12 Inches

13 inches

14 inches

15 inches

16 inches

The formula for the perimeter of a pentagon is expressed with the formula;

P = 5a

Given that the parameter are;

Since the sides are consecutive integers, then;

60 = 5(a)

expand the bracket

60= 5a

Make 'a' the subject

a = 12In

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Answer:

-9+3x

Step-by-step explanation:

(-3x2 + x + 5) − (4x2 − 2x)

(-6+x+5)-(8-2x)

(-1+x)-8+2x

-1+x-8+2x

-9+3x

Answer:

Step-by-step explanation:

Since the polynomial has a root of multiplicity 2 at x = 3, it can be written as (x - 3)^2 times another polynomial Q(x). Also, since it has roots of multiplicity 1 at x = 0 and x = -4, it can be written as (x - 3)^2 * (x - 0) * (x + 4) * Q(x).

Next, we can use the fact that the polynomial goes through the point (5, 144) to find the formula for Q(x). The polynomial P(x) must satisfy P(5) = 144, so we can write:

(5 - 3)^2 * (5 - 0) * (5 + 4) * Q(5) = 144

4 * 9 * 9 * Q(5) = 144

36 * Q(5) = 144

Q(5) = 4

So, the polynomial P(x) can be written as:

P(x) = (x - 3)^2 * (x - 0) * (x + 4) * 4

  = 4 * (x - 3)^2 * (x - 0) * (x + 4)

  = 4 * (x^2 - 6x + 9) * x * (x + 4)

  = 4x^4 - 84x^3 + 378x^2 - 648x + 576

This is the formula for P(x).

The number of pieces of candy that will be left on day 4 would be 2, 560 candies .

The number of pieces of candy left on day 8 would be 66 candies .

To find the number of candy left on the fourth day, given that Augustus only gives candies after the pile of 100, 000 candies is reached, the formula is:

= Number of starting candy x ( 1 - Percent given away ) ^ number of days

= 100, 000 x ( 1 - 60 % ) ⁴

= 100, 000 x 40 % ⁴

= 2, 560 candies

On Day 8, this would be:

= 100, 000 x ( 1 - 60 % ) ⁸

= 66 candies

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The question is:

How many pieces of candy will be left on day 4? On day 8?

Answer:

12

Step-by-step explanation:

3+2+7=12

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The simplification of the given expression would be = 210

A fraction is defined as the expression of part of a whole value in the form of a denominator and a numerator.

The above statement can be expressed above mathematically as follows:

= 7/8 × 16 × 1/2× 30

= 3360/16

= 210

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<1 + <4 = 180 supplementary angles

180 - 95 = 85 degrees

Answer:

Standard form of the equation for the circle

(x + 3)² + (y + 5)² = 40

Step-by-step explanation:

The equation of a circle in standard form is
[tex]\boxed{(x - a)^2 + (y-b)^2= r^2}[/tex]

where (a, b) is the center of the circle and r is the radius

To find center of circle

The end points of the diameter are (-5, -11) and (-1, 1)

The center of the circle is midway between these two points

The x-coordinate of the midpoint = (-5 + -1)/2 = -6/2 = -3

The y-coordinate of the midpoint is (-11 + 1) /2 = -10/2 = -5

So the center of the circle is at (-3, -5)

To find the radius,

Calculate the distance from (-3, -5) to any of of the endpoints.

Let's take the endpoint (-1, 1) and find its distance from (-3, -5)

The distance between any two points (x₁, y₁) and (x₂, y₂) is calculated from the formula

[tex]d^2 = {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2[/tex]

Substituting
(x₁, y₁) = (-1, 1)
(x₂, y₂)  = (-3, -5)

and r for distance

we get

[tex]r^2 = {(-3 - (-1))^2 + (-5 - 1)^2[/tex]

[tex]r^2 = {(-2)^2 + (-6)^2}[/tex]

[tex]r^2 = {{4} + {36}}[/tex]

[tex]r^2 = {40}[/tex]

So the center (a, b) is (-3, -5) and r² =40

Plugging this into the circle equation:
(x - (-3))² + (y - (-5))² = 40

(x + 3)² + (y + 5)² = 40

Answer:

Step-by-step explanation:

6x4=24

another way of writing it is using addition

add 4, six times

so

4+4+4+4+4+4

6 boxes each has four cakes

On solving the provided question we can say that  the area of a decagon is 5a2/2 × √5+2√5 5 + 2 5 ,

A decagon in geometry is a decagon or not. A basic decagon has 144° of inner angles added up. A decagram is a self-intersecting regular decagon. A decagon is a polygon that has ten sides, ten internal angles, and ten vertices. A decagon or decagon is a shape that may be found in geometry. Furthermore, it has 10 horns and 10 horns. A 12-sided polygon is called a dodecagon. A regular polygon known as a regular dodecagon specifically has sides that are of the same length and angles that are uniformly spaced around a circle.

the area of a decagon is 5a2/2 × √5+2√5 5 + 2 5 ,

'a = side length of the decagon

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Answer:

C.Only Maryanne's equation has the same solution as the original equation.

The solution is : 39 is the solution to Mr. Smith's equation.

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.

here, we have,

given that,

the equation is:

(16-2w)^2 + (3y÷3z)

Let w=5 y=9 and z=3

(16-2*5)^2 + (3*9÷3*3)

PEMDAS says parentheses first

Multiply and divide in the parentheses

(16-10)^2 + (27÷9)

Then add and subtract in the parentheses

(6)^2 + (3)

Now the exponent

=36 +3

=39

Hence, The solution is : 39 is the solution to Mr. Smith's equation.

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complete question:

What is the solution to Mr. Smith's equation?

Jenny's average jogging speed in the distance covered is; 10 miles/hr

Let x miles/hr be the speed that Jenny walks at

Then, 2x miles/hr is the speed that Jenny runs at

She jogs for  9.5 miles

2x miles = 1 hours

9.5 miles = a hours

a = 9.5/2x hours

She walks for 2.5 miles

x miles = 1 hour

2.5 miles = b

b = 2.5/x hours

Thus;

(9.5/2x) + (2.5)/x = 1.45

Multiply through by 2x to get;

9.5 + 5 = 2.9x

14.5/2.9 = x

x = 5 miles/hr

Jogging speed = 2 * 5 = 10 miles/hr

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Answer:

Step-by-step explanation:

To find the distance Tyler needs to swim, we can use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side, which is the hypotenuse.

In this case, the two shorter sides of the triangle are 40 feet and 80 feet, and the hypotenuse is the distance Tyler needs to swim to reach Jason. So we can write the equation as follows:

40^2 + 80^2 = d^2

where d is the distance Tyler needs to swim.

Expanding the equation:

1600 + 6400 = d^2

8000 = d^2

Taking the square root of both sides:

d = sqrt(8000) = 80 * sqrt(2)

So, Tyler needs to swim a distance of 80 * sqrt(2) feet, or approximately 113.1 feet, to reach Jason.

The perimeter of the pentagon PQRST will be equal to the perimeter of the pentagon ABCDE.

The regular polygon's edges are all identical to one another. The relationship between the number of sides to the mean distance determines the regular polygon's perimeter when it has n sides.

Then the perimeter of the pentagon ABCDE is given as,

P = AB + BC + CD + DE + EA

And the perimeter of the pentagon PQRST is given as,

P = PQ + QR + RS + ST + TP

Regular pentagons ABCDE and PQRST are congruent with each other.  Then the perimeter of the pentagons will be identical to each other.

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Answer:

  3 : 4

Step-by-step explanation:

You want to know the ratio of areas of a rectangle and square such that the rectangle is 50% longer and 50% narrower than the square.

A square that is 2 units on a side will be transformed to a rectangle that is 1.5×2 = 3 units long, and 0.5×2 = 1 unit wide.

The rectangle area is 3×1 = 3. The square area is 2×2 = 4.

The ratio of areas is ...

  rectangle area : square area = 3 : 4

Answer:

Derek's mango juice will last for 10 days.

Step-by-step explanation:

Derek buys 5 small bottles of mango juice, so he has 5 bottles in total.

He plans to drink half the contents of each bottle every morning, which means he will drink 1/2 * 1 bottle = 1/2 bottle of mango juice every day.

Since Derek drinks 1/2 bottle of mango juice every day, the 5 bottles of mango juice will last for 5 bottles / (1/2 bottle per day) = 10 days.

So, the answer is that the 5 bottles of mango juice will last for 10 days.

Hi there, here's your answer:

Given Derek buys 5 small bottles of Mango Juice
Also given that Derek drinks half a bottle every morning.

So taking the number of days to be 'x'

We get an equation [tex]\frac{1}{2} x = 5[/tex]

Upon cross multiplication, we get 1 × x = 5 × 2 = 10 days.

Therefore, the mango juice will last for 10 days.

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Answer:

choice C.  y = -4/3x + 2

Step-by-step explanation:

slope of a line perpendicular to another line has a slope that is the negative reciprocal of the slope of the first line.

m = -4/3  (negative reciprocal of 3/4)

Now use point-slope form to find the y-intercept (b):

y-2 = -4/3(x-0)

y = -4/3x + 2

From given quadratic equation:

Exact Cost of 31st food processor = $15.6

Approx. cost of 31st food processor  =  $15.2

What is a quadratic equation?

The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).

It is given that the quadratic equation has two roots. Roots might have either a real or imaginary nature.

The given quadratic equation for the cost of producing x food processors is:

 C(x) = 2400 + 40x - 0.4x²

a) The exact cost of producing the 31st food PROCESSOR is:

cost of 31 food processors - cost of 30 food processors = C(31) - C(30)

= (2400 + 40*31 - 0.4*31²) - (2400 + 40*30 - 0.4*30²)

= 3255.6 - 3240 = $15.6

b) The marginal cost at x = 31

Differentiate the quadratic equation

C'(x) = 40 - 0.8x

Marginal cost = C'(31) = 40 - 0.8*31 = $15.2

So the cost of producing the 31st food processor is approx $15.2.

Therefore from the given quadratic equation:

Exact Cost of 31st food processor = $15.6

Approx. cost of 31st food processor  =  $15.2

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