Eva is packing for a camping trip. There are 3 sleeping bags and 2 pillows to choose from. For the tent, Eva has 6 options. In how many different ways can Eva pick a set of camping gear that includes one of each item?

the probability of Jacinta selecting a green marble is 5/11. The total number of marbles in the bag is:

2 (blue) + 4 (red) + 5 (green) = 11

The probability of selecting a green marble can be found by dividing the number of green marbles by the total number of marbles:

P(selecting a green marble) = number of green marbles / total number of marbles

= 5 / 11

Therefore, the probability of Jacinta selecting a green marble is 5/11. Answer: 5/11.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

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If the cost price of the goods is R200 and they are sold at a mark-up of 100%, then the selling price is equal to the cost price plus the mark-up, or:

Selling price = Cost price + Mark-up

Mark-up = 100% x Cost price

= 100% x R200

= R200

So the mark-up is R200.

Selling price = Cost price + Mark-up

= R200 + R200

= R400

Therefore, the selling price of the goods is R400.

The other solutions are not viable because either they exceed the maximum number of hours Aisha can work (20 hours) or they do not meet the minimum amount Aisha needs to earn ($150).

If the ongoing research is successful, this approach might be an effective remedy. The only real way to resolve the problem is through negotiations between the military administration and the various opposition movements.

Part A: The correct system and graph to represent Aisha's situation is:

r + m ≤ 20 (maximum number of hours Aisha can work)

7r + 8.5m ≥ 150 (minimum amount Aisha needs to earn)

Part B: The viable solutions are:

r = 20, m = 0 (Aisha works only regular hours for 20 hours at $7 per hour)

r = 14, m = 6 (Aisha works 14 regular hours and 6 early morning hours at $7 per hour and $8.50 per hour, respectively)

r = 0, m = 18 (Aisha works only early morning hours for 18 hours at $8.50 per hour)

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Answer:

P= 40 ft

Step-by-step explanation:

Perimeter is the sum of all the lengths

So,

Perimeter= 6+4+15+10ft

= 35ft

Nearest ten can be 40ft or 30ft

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Harris ate x - 111 slices of pizza, So the total number of slices in the pizza is n ,where x is the number of slices each of the 44 friends received, and n is the total number of slices in the pizza, which must be a multiple of 44.

Let x be the number of slices each of the 44 friends received, then the total number of slices in the pizza is 44x. Since the pizza is evenly divided, the number of slices must be a multiple of 44.

Let y be the number of slices Harris received. Then, according to the problem, Harris ate 111 fewer slices than he received, so the number of slices he ate is y - 111.

Since the total number of slices in the pizza is 44x, we have:

y + 43x = 44x

Simplifying this equation, we get:

y = x

Therefore, Harris received the same number of slices as each of the other friends. So the number of slices he ate is:

y - 111 = x - 111

Substituting y = x, we get:

x - 111

Therefore, Harris ate x - 111 slices of pizza.

To find the value of x, we need to know the total number of slices in the pizza, which must be a multiple of 44. We can express this as:

44n = 44x

Dividing both sides by 44, we get:

n = x

So the total number of slices in the pizza is n.

Putting everything together, we get: Harris ate x - 111 slices of pizza, where x is the number of slices each of the 44 friends received, and n is the total number of slices in the pizza, which must be a multiple of 44.

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The probability that student A or B can solve a problem chosen at random is 0.95.

Probability is calculated by dividing the number of favourable outcomes by the number of possible outcomes.

Random: An event is referred to as random when it is not possible to predict it with certainty. The probability that either student A or B will be able to solve a problem chosen at random can be calculated as follows:

P(A or B) = P(A) + P(B) - P(A and B) where: P(A) = probability of A solving a problem = 0.75, P(B) = probability of B solving a problem = 0.7, P(A and B) = probability of both A and B solving a problem. Since A and B are independent, the probability of both solving the problem is:

P(A and B) = P(A) x P(B) = 0.75 x 0.7 = 0.525

Now, using the above formula: P(A or B) = P(A) + P(B) - P(A and B) = 0.75 + 0.7 - 0.525 = 0.925

Therefore, the probability that student A or B can solve a problem chosen at random is 0.95 (or 95%).

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Answer:

[tex] |x - 300| \leqslant 10[/tex]

The zero vector: The zero vector 0 = [0,0;0,0;0,0] is also a member of W. Thus, the third criterion is satisfied.

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Mails consumed a total of 5000 ml of liquid on the road.

First, let's understand what is meant by "total." Total refers to the sum of all the individual quantities of liquid that Mails consumed. In this case, we are trying to find the total amount of liquid that Mails consumed.

Next, we need to know that 1 liter is equal to 1000 milliliters (ml). This is an important conversion factor that we will use to convert half-liters to milliliters.

Now, we can start to solve the problem. We know that Mails used 10 half-liter hotties of liquid on the road. To convert half-liters to milliliters, we need to multiply by 500 (since half a liter is 500 milliliters). So, we can calculate the total amount of liquid that Mails consumed as follows:

Total amount of liquid = 10 x 500 ml/hottie

Total amount of liquid = 5000 ml

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Answer:

The solution set is (13,− 32). A quadratic equation of the form x 2= k can be solved by factoring with the following sequence of equivalent equations.

Step-by-step explanation:

The rate at which the amount of bacteria is changing after 12 hours is 21.698 units/hour.

The given formula for the amount of bacteria present in a medium after t hours is:

[tex]a(t) = 16e^ (0.32t)[/tex]

Now, we need to find out at what rate the amount of bacteria is changing after 12 hours.

This means we need to find out the derivative of a(t) with respect to t and then substitute t = 12 in the derivative formula to get the rate of change of bacteria after 12 hours.

Differentiating the given formula for a(t) with respect to t, we get:

a'(t) = [tex]16(0.32)e^(0.32t)[/tex]

On substituting, t = 12, we get

a'(12) = [tex]16(0.32)e^ (0.32X12)[/tex]

On solving this, we get a'(12) = 21.698.

Therefore, the rate at which the amount of bacteria is changing after 12 hours is 21.698 units/hour.

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According to a census, 3.3% of all births in a country are twins. In a month, there are 2,500 births. The census reports that 3.3% of all births result in twins, and the probability of having more than 90 twins in a month is "0.4351."

We will solve this problem using the binomial distribution formula, which is as follows:P (X > 90) = 1 - P (X ≤ 90)where P represents the probability, X represents the number of twins born in a month, and X is a binomial random variable with a sample size of n = 2,500 and a probability of success (having twins) of p = 0.033. Using the TI-83 calculator, TI-83 Plus, or TI-84 calculator, the following steps can be followed:

Press the "2nd" button followed by the "VARS" button (DISTR) to access the distribution menu. Scroll down and select "binomcdf (" from the list of options (use the arrow keys to navigate). The binomcdf ( menu will appear on the screen. The first number in the parentheses is the number of trials, n, and the second number is the probability of success, p. We want to find the probability of having more than 90 twins, so we need to use the "compliment" option. Therefore, we will subtract the probability of having 90 twins or less from 1 (using the "1 -" key). Type in "binomcdf (2500,0.033,90)" and press the "ENTER" button on your calculator.

This will give you the probability of having 90 twins or fewer in a month. Subtract this value from 1 to obtain the probability of having more than 90 twins in a month, which is the answer to our question. P(X>90) = 1 - binomcdf (2500,0.033,90)P(X>90) = 1 - 0.5649P(X>90) = 0.4351Therefore, the probability of having more than 90 twins in a month is 0.4351.

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The volume of the frustum is 970 cm².

What is frustum?

In geometry, a frustum is a three-dimensional solid that is created by cutting a larger solid, such as a cone or pyramid, with a plane parallel to its base, and then removing the smaller solid that lies above the plane. The resulting solid has two parallel bases of different sizes, and its sides are trapezoidal in shape.

We know that, volume of frustum is given by

                       V = (1/3) * h * (A + B + sqrt(A * B))

where V is the volume of the frustum, h is the height of the frustum, A is the area of the rectangular base, and B is the area of the rectangular top.

So, A = base × height = 8 × 16

                                    = 128 cm²

Similarly, B = base × height =  3 × 6

                                             = 18 cm²

and, given height of frustum = 15 cm

Now, putting all values into the formula:

So,  V = (1/3)× h × (A + B + sqrt(A×B))

          = 1/3 × 15 × ( 128+18 + √(128×18))

          = 5 × ( 146 + 48 )

          = 970 cm²

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Answer:

10 units

Step-by-step explanation:

Here, legs = base and perpendiculars.

So, Clearly given Base = 6 units Perpendicular = 8 cm

Square's Side = Hypotenuse.

By Pythagoras theorem,

H² = B²+P²

H ² = 6²+8²

H² = 36+64 = (10)²

H = 10 units.

Square's Side length = 10 units

Answer:

Step-by-step explanation:

You need to find the volume if one shoe box by doing:

Length x Width x Height

Of the shoe box

Then multiply by 30 to get the volume for all the shoe boxes

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The following characteristics of racional decimal number abstraction apply: Conmutative property: The order of the remaining rational decimal numbers has no bearing on the operation's outcome,

Proprietary property: The racional decimal numbers may remain in various groups without affecting the operation's ultimate outcome, i.e., (a - b) - c = a - (b - c). Distributive property: Subtracting one racional decimal number from a sum of racional decimal numbers equals the sum of the subtractions of each one of them, or a - (b + c) = a - b - c. Neutral element: If a racional decimal number is left at zero, the outcome is the same number, i.e., a - 0 = a. Estas propiedades son útiles para simplificar y realizar cálculos más complejos con números racionales decimales.

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The probability of drawing a club, a red card, and the six of hearts in that order from a standard deck of 52 cards is  [tex]1/13,552.[/tex]

This is because the probability of drawing a club is 1/4, and the probability of drawing a red card is 1/2, and the probability of drawing the six of hearts is 1/52.
Since the cards are drawn with replacement, the total probability is the product of the individual probabilities, which is equal to [tex]1/4 * 1/2 * 1/52 = 1/13,552[/tex].
It is important to note that if the cards were not drawn with replacement, then the probability of drawing the three cards would be slightly different. The total probability would be equal to [tex]1/4 * 1/2 * 1/51 = 1/12,600.[/tex]
It is also important to note that since this is a probability question, the answer can be expressed as a decimal or percentage. In decimal form, the probability of drawing the three cards is 0.000074, and in percentage form, the probability of drawing the three cards is 0.0074%.

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Thus, the probability are Zero represents the impossibility.

1/2 equals probable and unlikely

1 = event happens.

Because we don't know how something will turn out, we might talk about the probability of one outcome or the potential for several outcomes.

Typically, the likelihood is stated as the proportion of favourable events to all other potential outcomes in the sample space.

The probability of an event is calculated using the formula P(E) = (Number of favourable outcomes) (Sample space).

Given that probability can only be a number between 0 and 1,

The zeroth value is the impossible.

so there is a 50% chance for both likely and unlikely.

If 1, the event must take place.

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The Trapezoidal rule and Simpson's rule are two methods used to approximate the value of a definite integral. The Trapezoidal rule approximates the integral by dividing the region between the lower and upper limits of the integral into n trapezoids, each with a width h. The approximate value of the integral is then calculated as the sum of the areas of the trapezoids. The Simpson's rule is similar, except the region is divided into n/2 trapezoids and then the integral is approximated using the weighted sum of the area of the trapezoids.

For the given integral 4 x x2 1 0 dx, with n = 200, the Trapezoidal rule and Simpson's rule approximate the integral to be 7.4528 and 7.4485 respectively, rounded to four decimal places. The exact value of the integral is 7.4527. The difference between the exact and approximate values is very small, thus indicating that both the Trapezoidal rule and Simpson's rule are accurate approximations.

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The value of the double integral using the easier order, ydA bounded by y = x − 6; x = y² is 125/12.

The double integral, indicated by ', is mostly used to calculate the surface area of a two-dimensional figure. By using double integration, we may quickly determine the area of a rectangular region. If we understand simple integration, we can easily tackle double integration difficulties. Hence, first and foremost, we will go over some fundamental integration guidelines.

Given, the double integral ∫∫yA and the region y = x-6 and x = y²

y = x-6

x = y²

y² = y +6

y² - y - 6 = 0

y² - 3y +2y - 6 = 0

(y-3) (y+2) = 0

y = 3 and y = -2

[tex]\int\int\limits_\triangle {y} \, dA\\ \\[/tex]

= [tex]\int\limits^3_2 {y(y+6-y^2)} \, dx \\\\\int\limits^3_2 {(y^2+6y-y^3)} \, dx \\\\(\frac{y^3}{3} + 3y^2-\frac{y^4}{4} )_-_2^3\\\\\frac{63}{4} -\frac{16}{3} \\\\\frac{125}{12}[/tex]

The value for the double integral is 125/12.

Integration is an important aspect of calculus, and there are many different forms of integrations, such as basic integration, double integration, and triple integration. We often utilise integral calculus to determine the area and volume on a very big scale that simple formulae or calculations cannot.

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A system of linear inequalities that the graph represent include the following:

x ≥ 4.

y < -x - 2

y ≥ 3x + 3

y > x - 4

In Mathematics, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

At data points (-3, 0) and (0, 3), the slope of this line can be calculated as follows;

Slope = (3 - 0)/(0 + 3) = 3/3 = 1

y-intercept = 3.

Therefore, a linear inequality that models the line is given by:

y ≥ 3x + 3

At data points (-2, 0) and (0, -2), the slope of this line can be calculated as follows;

Slope = (-2 - 0)/(0 + 2) = -2/2 = -1

y-intercept = -2.

Therefore, a linear inequality that models the line is given by:

y < -x - 2

At data points (4, 0) and (0, -4), the slope of this line can be calculated as follows;

Slope = (-4 - 0)/(0 - 4) = -4/-4 = 1

y-intercept = -4.

Therefore, a linear inequality that models the line is given by:

y > x - 4

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Answer: 23 degrees

Step-by-step explanation:

Assuming that 117 is the entire angle we can find that:

94+x = 117

Subtract 94 from both sides:

x = 117-94

x = 23 degrees

(a) The probability that exactly two cars finish the race is 0.0512.

(b) The probability that at most two cars finish the race is 0.05792.

(c) The probability that at least three cars finish the race is 0.94208.

(a) To determine the probability that exactly two cars finish the race, we have to use binomial distribution. In this case, we have n = 5 trials, and p = 0.8 is the probability that a car finishes the race (1 - 0.2). Using the binomial distribution formula:

P(X = k) = (nCk)(p^k)(1 - p)^(n - k)

Where X is the number of cars that finish the race, we get:

P(X = 2) = (5C2)(0.8²)(0.2)³= (10)(0.64)(0.008)= 0.0512

Therefore, the probability that exactly two cars finish the race is 0.0512.

(b) To determine the probability that at most two cars finish the race, we have to calculate the probabilities of 0, 1, and 2 cars finishing the race and add them up.

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)= (5C0)(0.8⁰)(0.2)⁵ + (5C1)(0.8¹)(0.2)⁴ + (5C2)(0.8²)(0.2)³= 0.00032 + 0.0064 + 0.0512= 0.05792

Therefore, the probability that at most two cars finish the race is 0.05792.

(c) To determine the probability that at least three cars finish the race, we can calculate the probability of 0, 1, and 2 cars finishing the race and subtract it from 1, which gives us the probability of at least three cars finishing the race.

P(X ≥ 3) = 1 - [P(X = 0) + P(X = 1) + P(X = 2)]= 1 - (0.00032 + 0.0064 + 0.0512)= 0.94208

Therefore, the probability that at least three cars finish the race is 0.94208.

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We cannot prove that the quadrilateral is a parallelogram with only the given information that AB = DC.

What is quadrilateral and parallelogram ?

A quadrilateral is a four-sided polygon, which means it is a closed shape with four straight sides. Some examples of quadrilaterals include rectangles, squares, trapezoids, and rhombuses.

A parallelogram is a special type of quadrilateral where both pairs of opposite sides are parallel. This means that the opposite sides never intersect, and they have the same slope. Additionally, the opposite sides of a parallelogram are congruent (i.e., have the same length), and the opposite angles are also congruent. Some examples of parallelograms include rectangles, squares, and rhombuses.

To prove that a quadrilateral is a parallelogram, we need to show that both pairs of opposite sides are parallel. Knowing that AB = DC only gives us information about the lengths of the sides, but it doesn't tell us anything about their orientation or whether they are parallel.

We would need additional information, such as the measures of angles or the lengths of other sides, to determine whether the quadrilateral is a parallelogram.

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Answer:

  3. 79.9 mm²

  4. 6.4 in

  5. 177.5 mi²

  6. 60.3°

Step-by-step explanation:

Given various quadrilaterals and their dimensions, you want to find missing dimensions.

In all cases, one or more area formulas and trig relations are involved. The trig relations are summarized by the mnemonic SOH CAH TOA. The relevant relation for these problems is ...

  Tan = Opposite/Adjacent

It is also useful to know that 1/tan(x) = tan(90°-x).

The formula for the area of a trapezoid is ...

  A = 1/2(b1 +b2)h

The relevant formula here for the area of a parallelogram is ...

  A = bs·sin(α) . . . . . where α is the angle between sides of length b and s

Using the area formula above, we find the area to be ...

  A = (21 mm)(9 mm)·sin(155°) ≈ 79.9 mm²

The area is about 79.9 square mm.

The given figure shows two unknowns. We can write equations for these using the area formula and using a trig relation.

If we draw a vertical line through the vertex of the marked angle, the base of the triangle to the right of it is (b2-4). The acute angle at the top of that right triangle is (121°-90°) = 31°. The tangent relation tells us ...

  tan(31°) = (b2 -4)/h   ⇒   h = (b2 -4)/tan(31°)

Using the area formula we have ...

  A = 1/2(b2 +4)h

and substituting for A and h, we get ...

  20.8 = 1/2(b2 +4)(b2 -4)/tan(31°)

  2·tan(31°)·20.8 = (b2 +4)(b2 -4) = (b2)² -16 . . . . . multiply by 2tan(31°)

  (b2)² = 2·tan(31°)·20.8 +16 . . . . . . . add 16

  b2 = √(2·tan(31°)·20.8 +16) ≈ 6.4 . . . . . . take the square root

Base 2 of the trapezoid is about 6.4 inches.

To find the area, we need to know the height of the trapezoid. To find the height we can solve a triangle problem.

If we draw a diagonal line parallel to the right side through the left end of the top base, we divide the figure into a triangle on the left and a parallelogram on the right. The triangle has a base width of 10 mi, and base angles of 60° and 75°.

Drawing a vertical line through the top vertex of this triangle divides it into two right triangles of height h. The top angle is divided into two angles, one being 90°-60° = 30°, and the other being 90°-75° = 15°. The bases of these right triangles are now ...

and their sum is 10 mi.

The height h can now be found to be ...

  h·tan(30°) +h·tan(15°) = 10

  h = 10/(tan(30°) +tan(15°))

Back to our formula for the area of the trapezoid, we find it to be ...

  A = 1/2(b1 +b2)h = 1/2(20 +10)(10/(tan(30°) +tan(15°)) ≈ 177.5

The area of the trapezoid is about 177.5 square miles.

The final formula we used for problem 5 can be used for problem 6 by changing the dimensions appropriately.

  A = 1/2(b1 +b2)(b1 -b2)/(tan(90-x) +tan(90-x))

  112 = 1/2(20+12)(20-12)/(2·tan(90-x)) = (20² -12²)·tan(x)/4

  tan(x) = 4·112/(20² -12²)

  x = arctan(4·112/(20² -12²)) = arctan(7/4) ≈ 60.3°

Angle x° in the trapezoid is about 60.3°.

__

Additional comment

There is no set "step by step" for solving problems like these. In general, you work from what you know toward what you don't know. You make use of area and trig relations as required to create equations you can solve for the missing values. There are generally a number of ways you can go at these.

A nice scientific calculator has been used in the attachment for showing the calculations. A graphing calculator can be useful for solving any system of equations you might write.

The second attachment shows a graphing calculator solution to problem 5, where we let y = area, and x = the portion of the bottom base that is to the left of the top base. Area/15 represents the height of the trapezoid. This solution also gives an area of 177.5 square miles.

The value of (37)-2 is 1/1369, in its simplest form as an improper fraction.

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. In other words, it is a fraction that is larger than a whole number.

When an expression is written in the form of [tex]x^{(-n)[/tex], it means the reciprocal of [tex]x^n.[/tex] In this case, we have the expression[tex](37)^{(-2)[/tex] which means the reciprocal of 37².

The expression (37)-2 means 37 raised to the power of -2, or 1/(37²). To simplify this fraction, we can multiply the numerator and denominator by 1,296 (37²):

1/(37²) = 1 * 1 / (37 * 37)

= 1/1369

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Answer:

x=33

Step-by-step explanation:

all angles in a triangle sum to 180 degrees

x+2x+(2x+15) = 180 <---- simplify this

5x+15 = 180

5x=165

x = 33

Answer:

5.333 hours

Step-by-step explanation:

We know

4 Pipes fill a tank in 16 hours.

How long will it take to fill the tank if 12 pipes of the same dimensions are used?

We Take

16 x 1/3 = 5.333 hours

So, it takes about 5.333 hours to fill the tank.

According to the solving  function f could describe the bacteria population d days after the scientists first measured it, assuming it grows exponentially F(d) = 10000 - a[tex]^\frac{d}{5}[/tex].

A mathematical expression, rule, or law known as a function defines the relationship between two independent variables and a dependent variable (the dependent variable). In mathematics, functions are often utilised, and they are essential for creating physical connections in the sciences.

Substituting d = 5 and f(d)

Solution: fid) = 10000⋅ ad

{substitute d=5 and fid)=20000 into fid=10000. ady

10000- a⁵ =20000

a⁵ =2[tex]^\frac{1}{5}[/tex]

a = 2

F(d) = 10000 - a[tex]^\frac{d}{5}[/tex]

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