Write an equation for a line that is parallel to 9x + 3y = 8 and passes through the point (-1, -4).

The number of edges that the prism has is

When a plane intersects a prism, the shape formed is known as the cross section. The cross section of the prism will have the same form as the base if it is divided by a plane that runs horizontally and parallel to the base.

A prism is a 3-dimensional object with two congruent and parallel bases (which are polyggonal) connected by rectangular lateral faces. The number of edges of a prism is equal to the sum of the number of edges of the two bases and the number of lateral faces.

Each base of the prism has n edges, so the two bases together have 2n edges. The number of lateral faces of the prism is equal to the number of edges of one of its bases, so there are n lateral faces. Each lateral face has 4 edges, so the total number of edges of the lateral faces is 4n.

Therefore, the total number of edges of the prism is equal to the sum of the number of edges of the two bases (2n) and the number of lateral faces (4n), which is 2n + 4n = 6n.

In conclusion, the cross section of a prism is an n-sided polygon and the prism has n + 2 edges.

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Using the expression, 15x + 7y = 208 there were x = 12 baby dinosaurs and y = 4 adult dinosaurs.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

Each baby dinosaur made 15 paintings and every adult dinosaur made 7 paintings.

The total number of paintings the entire herd made is 208.

There were 3 times as many baby dinosaurs as adult dinosaurs.

Now, let x be the number of baby dinosaurs and y be the number of adult dinosaurs.

Then,

x = 3y

So,

The expression for the total number of paintings will be:

208 = 15x + 7y

208 = 15(3y) + 7y

208 = 45y + 7y

208 = 52y

y = 4

So,

x = 3y = 3(4) = 12

There were 12 baby dinosaurs and 4 adult dinosaurs.

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Answer:

V = 1046.9

Step-by-step explanation:

The equation for volume is (4/3)pi r^3

substitute 3.14 in for pi and 6.3 in for r so (4/3)*3.14*6.3^3

Answer:

La masa de 10⁹ μm³ de agua es 1 mg.

Step-by-step explanation:

La densidad del agua es:

\( d = \frac{m}{V} = 1000 kg/m^{3} \)

En donde:

m: es la masa =?

V: es el volumen = 10⁹ μm³

Para encontrar la masa de agua debemos convertir las unidades del volumen de μm³ a m³:

\(V = 10^{9} \mu m^{3}*\frac{1 m^{3}}{(10^{6} \mu m)^{3}} = 10^{-9} m^{3}\)

Ahora, la masa es:

\(m = d*V = 1000 kg/m^{3}*10^{-9} m^{3} = 10^{-6} kg = 10^{-3} g = 1 mg\)                      

Por lo tanto, la masa de 10⁹ μm³ de agua es 1 mg.

Espero que te sea de utilidad!          

The probability of being dealt a straight flush in a 5-card poker hand from a regular 52-card deck is approximately 0.00001539, or about 0.001539%

A straight flush consists of five cards in a sequence and of the same suit. We need to consider the number of possible straight flush hands.

There are 10 possible sequences in a suit (A-2-3-4-5, 2-3-4-5-6, ..., 10-J-Q-K-A). For each sequence, there are four possible suits. Therefore, there are a total of 40 possible straight flush hands in the deck (10 sequences * 4 suits).

The total number of possible 5-card hands is given by the combination formula: C(52, 5) = 2,598,960. This represents the number of ways to choose 5 cards out of the 52-card deck.

Now, we can calculate the probability:

Probability of straight flush = (Number of favorable outcomes) / (Total number of possible outcomes)

Probability of straight flush = 40 / 2,598,960

Probability of straight flush ≈ 0.00001539

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Answer: Your answer is B

Step-by-step explanation:

Option B) A₁ = 50.3in², A₂ = 113.1in², A₃ = 176.7in² is the correct answer.

A circle is simply a closed 2-dimensional curved shape with no edges or corners.

Area of a circle is expressed as;

A = πr²

Where r is the radius of the circle and π is pi ( π = 3.14159 ).

For cake A;

From the previous expression of area of a circle

Area of A = πr²

Area of A = 3.14159 × (4in)²

Area of A = 3.14159 × 16in²

Area of A = 50.23in²

Hence, the area of the first cake is 50.23in².

For cake B;

From the previous expression of area of a circle

Area of B = πr²

Area of B = 3.14159 × (6in)²

Area of B = 3.14159 × 36in²

Area of B = 113.1in²

Hence, the area of the second cake is 113.1in².

For cake C;

From the previous expression of area of a circle

Area of C = πr²

Area of C = 3.14159 × (7.5in)²

Area of C = 3.14159 × 56.25in²

Area of C = 176.7in²

Hence, the area of the third cake is 176.7in².

Option B) A₁ = 50.3in², A₂ = 113.1in², A₃ = 176.7in² is the correct answer.

Hence;

Area of the first cake is 50.23in².

Area of the second cake is 113.1in².

Area of the third cake is 176.7in².

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Answer:Andrew tarda 19 minutos en ducharse y desayunar

Explicación paso a paso:

720 seg de ducharse + 420 segundos de su desayuno dan igual a 1140 segudnos

a este numero de segundos hay que pasarlo a minutos. El resultado es 19 minutos que son 1140 segundos

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

3:2 is equal to 18:12 not 17

Answer:

x=80 y=80

Step-by-step explanation:

x must be 80 because with an interception like this the angles that are opposite of each other will be the same degrees.

y must be 80 because it has a line parallel to the line that 80 is on

Answer: 51.75

Step-by-step explanation: 15 precent of 45 is 6.75

                                              Then add 45+6.75

Answer:

Her total including the bill will be $51.75

Step-by-step explanation:

15% of $45

= $6.75

$45 + $6.75 = $51.75

The multiplication expression will be (9*3+1)/3.

What exactly are expressions?

In mathematics, an expression is a combination of one or more numbers, variables, and/or mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and logarithms) that can be evaluated to produce a single numerical or algebraic value.

Expressions can be very simple, such as a single number or variable, or they can be more complex, involving multiple variables and operations. They can also include mathematical functions and constants, such as pi or the square root of a number.

Here are some examples of expressions in mathematics:

Now,

We have expression 9 1/3

and to change it to simple fraction

we do this 9*3+1/3

=27+1/3

=28/3

Hence,

           The multiplication expression will be (9*3+1)/3.

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The confidence associated with an interval estimate is called the confidence level.

When making an interval estimate, such as estimating a population parameter based on a sample, it is important to provide an indication of the level of confidence we have in the estimate. The confidence level represents the probability or level of certainty that the true population parameter falls within the calculated interval.

For example, if we calculate a 95% confidence interval for the mean height of a population, it means that we are 95% confident that the true population mean height lies within that interval. This implies that if we were to repeat the sampling and interval estimation process multiple times, approximately 95% of the intervals would contain the true population parameter.

The confidence level is typically expressed as a percentage, such as 90%, 95%, or 99%. A higher confidence level indicates a greater level of certainty in the interval estimate but also results in a wider interval.

In summary, the confidence level associated with an interval estimate represents the level of confidence or probability that the interval contains the true population parameter.

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Answer:

900

Step-by-step explanation:

To find the number of 4-digit numbers divisible by both 2 and 5, we need to consider the numbers that are divisible by their least common multiple, which is 10.

The first 4-digit number divisible by 10 is 1000, and the last 4-digit number divisible by 10 is 9990.

To calculate the count, we need to find the number of multiples of 10 between 1000 and 9990 (inclusive). We can divide the difference between these two numbers by 10 and add 1:

(9990 - 1000) / 10 + 1 = 8990 / 10 + 1 = 899 + 1 = 900

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Answer:

the volume of cylinder = πr²h

h = 5cm

r = 6cm

volume = π × 6² × 5

= π × 6 × 6 × 5

= 180πcm³

Solution :

Given :

Perimeter, P = 16 m

The length is 4 times less then three times the width.

Let the length be l and width be w.

Therefore, according to the equation :

Length, l = 3w -  4  ................(i)

Perimeter, P  = 2(l+w)

                 16 = 2(l+w) ............(ii)

                 16 = 2l + 2w

                  8 = l + w ..............(iii)

Therefore solving equation (i) and (iii)

l = 3w - 4

8 = l + w

We get, w = 3  and l = 5

Answer:

16 divided by 3 = 5.3

Step-by-step explanation:

Answer:

if the lines have arrows at the end then the domain is infinite.

Step-by-step explanation:

Lines are infinite

Answer:

Domain: x ∈ all real numbers

Step-by-step explanation:

It appears to be the function |x|-1 and that is defined by all values of x. Meaning that the domain is x can be any value.

The correct term to complete the sentence is "rational expression." A rational expression has a fraction in its numerator, denominator, or both.

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The formula to determine the area of a rectangle is:

Where

A is the area

w is the width of the rectangle

l is the length of the rectangle

If you know the area and the length of the rectangle, you can determine its width. First, write the formula for w, to do so, divide both sides of the equal sign by l

If A= 7448m² and l=98m, then you can calculate the width as follows:

The width of the parking lot is 76 meters

Answer:

30

Step-by-step explanation:

Okay, to find the number of balloons left over, disregard the number of kids and focus only on 150 balloons and that only 4/5 were "smashed." Multiply 150 by 4/5 to find the amount of balloons used, which is 120, and find the difference between 150 and 120, which is 30.

The solution of initial value problem, y = 9/t - 1, t ≠ 0.

We can begin by rearranging the equation and separating the variables:

t^2 dy/dt - yt = t + 1

dy/(y+1) = (t+1)/t^2 dt

Integrating both sides, we get:

ln|y+1| = -1/t + t/t + C

ln|y+1| = -1/t + C

|y+1| = e^C /t

Using the initial condition y(1) = 8, we can find the value of C:

|8+1| = e^C /1

e^C = 9

C = ln 9

Substituting back into the general solution, we have:

|y+1| = 9/t

We can now solve for y in terms of t:

y+1 = ±9/t

If we take the positive sign, we get:

y = 9/t - 1

If we take the negative sign, we get:

y = -9/t - 1

Thus, the general solution to the initial value problem is:

y = 9/t - 1 or y = -9/t - 1

Using the initial condition y(1) = 8, we can see that the correct solution is:

y = 9/t - 1

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Answer:

$ 2,600

Step-by-step explanation:

It's given that 260 People donated $10 is to an organisation . We need to find the total money received by the organisation .

Here we just need to the number of people with the amount each person gave , that is ;

\(\implies \rm Total \ amount = \$ 10 \times 260 \\\\\rm\implies Total \ amount = \$ 2,600 \)

Hence the total money received by the organisation is $ 2600 .

The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.

To find the extreme values of V, we need to take the derivative of V and set it equal to zero. So, let's begin:

\(V(x) = x(10-2x)(16-2x)\)
Taking the derivative with respect to x:
\(V'(x) = 10x - 4x^2 - 32x + 12x^2 + 320 - 48x\)
Setting V'(x) = 0 and solving for x:
\(10x - 4x^2 - 32x + 12x^2 + 320 - 48x = 0\\8x^2 - 30x + 320 = 0\)
Solving for x using the quadratic formula:
\(x = (30 ± \sqrt{(30^2 - 4(8)(320))) / (2(8))\\x = (30 ± \sqrt{(1680)) / 16\\x = 0.93 or x =5.07\)
So, the extreme values of V occur at x ≈ 0.93 and x ≈ 5.07. To determine whether these are maximum or minimum values, we need to examine the second derivative of V. If the second derivative is positive, then the function has a minimum at that point. If the second derivative is negative, then the function has a maximum at that point. If the second derivative is zero, then we need to use a different method to determine whether it's a maximum or minimum.

Taking the second derivative of V:
V''(x) = 10 - 8x - 24x + 24x + 96
V''(x) = -8x + 106

Plugging in x = 0.93 and x = 5.07:
V''(0.93) ≈ 98.36 > 0, so V has a minimum at x ≈ 0.93.
V''(5.07) ≈ -56.56 < 0, so V has a maximum at x ≈ 5.07.

Now, to interpret these values in terms of the volume of the box, we need to remember that V(x) represents the volume of a box with length 2x, width 2x, and height x. So, the maximum value of V occurs at x ≈ 5.07, which means that the volume of the box is greatest when the height is about 5.07 units. The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.

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a) The extreme values of V are:

Minimum value: V(0) = 0

Relative maximum value: V(3) = 216

Absolute maximum value: V(4) = 128

b) The absolute maximum value of V at x = 4 represents the case where the box has a square base of side length 4 units, height 2 units, and width 8 units, which has a volume of 128 cubic units.

a) To find the extreme values of V, we first need to find the critical points of the function. This means we need to find where the derivative of the function equals zero or is undefined.

Taking the derivative of V(x), we get:

\(V'(x) = 48x - 36x^2 - 4x^3\)

Setting this equal to zero and solving for x, we get:

\(48x - 36x^2 - 4x^3 = 0\)
4x(4-x)(3-x) = 0

So the critical points are x = 0, x = 4, and x = 3.

We now need to test these critical points to see which ones correspond to maximum or minimum values of V.

We can use the second derivative test to do this. Taking the derivative of V'(x), we get:

\(V''(x) = 48 - 72x - 12x^2\)

Plugging in the critical points, we get:

V''(0) = 48 > 0 (so x = 0 corresponds to a minimum value of V)
V''(4) = -48 < 0 (so x = 4 corresponds to a maximum value of V)
V''(3) = 0 (so we need to do further testing to see what this critical point corresponds to)

To test the critical point x = 3, we can simply plug it into V(x) and compare it to the values at x = 0 and x = 4:

V(0) = 0
V(3) = 216
V(4) = 128

So x = 3 corresponds to a relative maximum value of V.
b) In terms of the volume of the box, the function V(x) represents the volume of a rectangular box with a square base of side length x and height (10-2x) and width (16-2x).
The minimum value of V at x = 0 represents the case where the box has no dimensions (i.e. it's a point), so the volume is zero.
The relative maximum value of V at x = 3 represents the case where the box is a cube with side length 3 units, which has a volume of 216 cubic units.
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Answer: $12.28

Step-by-step explanation:

Here's the complete question:

Three teachers bought prizes to put in a bin at school. Mrs. Maier spent $7.68 on stickers. Mr. Lang spent $11.52 on balloons. Mrs. Connor spent $17.64 on pencils. The teachers divided the cost evenly. How much did each teacher pay?

Cost of stickers = $7.68

Cost of balloons = $11.52

Cost of pencils = $17.64

Total spent = $7.68 + $11.52 + $17.64 = $36.84

The amount that each teacher will pay when the total cost is evenly shared will be:

= $36.84 / 3

= $12.28

Answer:

Step-by-step explanation:

tried my best as the first two got me stuck

wouldn't recommend trying my answer and Id wait for another answer

The required bearing angle of town B from Thomas is 75°.

We have,

Bearing is basically an angle that is measured clockwise from the north. Bearing are generally written in three figure.

Given that

Thomas is facing towards town A, which is at a bearing of 300°.

Implies that town A is 300° from north.

If Thomas turns 135° clockwise, then he faces towards town B,

The bearing angle will be 300+135 = 435°

Since, one complete round makes angle 360°, therefore

The required bearing angle = 435 - 360 = 75

The bearing angle of town B from Thomas is 75°.

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Answer:

a part

Step-by-step explanation:

Answer is attached....

Hope it helps:)

Answer:

You'd have to talk for 25 minutes for them to be the same

Step-by-step explanation:

15 + 0.25x

20 + 0.05x

Where x is the number of minutes

You'd have to talk for 25 minutes for them to be the same

Answer:

4C2 * 6C2 * 5C2

Step-by-step explanation:

White balls = 4

Yellow balls = 6

Red balls = 5

In other to select a total of 6 balls, of which there must be 2 balls each of color white, yellow and red :

That means :

2 red balls from 5 red balls = 5C2

2 balls for 6 yellow balls = 6C2

2 balls from 4 white balls = 4C2

To obtain the number of possible combinations, take the product of the three combinations :

4C2 * 6C2 * 5C2

If bag contains 4 white balls, 6 yellow balls, and 5 red balls then  6 balls can be chosen if there must be 2 balls of each color in 900 ways

permutation is way of selecting and arranging things while combination is way of selecting things .

Given that  bag contains 4 white balls, 6 yellow balls, and 5 red balls

we have to select 6 balls

it's given that there must be 2 balls of each color

So here's how we can select them

2 white balls ,2 yellow balls and 2 red balls

So we have to select 2 white balls out of 4  white balls ,2 yellow balls out of 6 yellow balls and 2 red balls out of 5 red balls

so number of ways of selecting

\({4 \choose 2} \times {6 \choose 2}\times {5 \choose 2}\)

\(=6\times15\times10\\\\=900\)

If bag contains 4 white balls, 6 yellow balls, and 5 red balls then  6 balls can be chosen if there must be 2 balls of each color in 900 ways

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