4. What is Probability?
(ii) State the axioms of probability
(iii)Two fair dice are thrown, what is the probability of getting
(a) the sum of 9
(b) two odd numbers
(c) two prime numbers
(d) two factors of 12
4c. What is Statistics?

The volume of the figure, by splitting it into two cuboids comes to be 3300 ft³.

The volume of a cuboid is the product of its three dimensions i.e. length, breadth, and height.

Let us split the given figure into two cuboids

So, the volume of the figure will be the sum of the volume of both the cuboids.

So, the volume of the cuboid with dimensions 20 ft x 25 ft x 5ft

= 20 x 25 x 5

=2500 ft³.

The volume of the cuboid with dimensions  4 ft x 25ft x 8ft

=4 x 25x 8

=800 ft³.

So, the volume of the figure = 2500 + 800 =3300 ft³.

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Answer:80

Step-by-step explanation:x is the original price.

x - .25*x is the sale price.

the sale price is 60.00

x - .25*x = 60

x - .25*x is equal to .75*x

.75*x = 60

divide both sides of this equation by .75 and you get:

x = 60/.75 = 80

the original price was 80

25% of 80 = 20

80 - 20 = 60

number look good.

solution is that the original price was 80 dollars.

Answer:

$178.20

Step-by-step explanation:

Because 10% + $162.00

It would be wiser for the couple to stay in the old apartment and save $1400.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Explanation:

If they stay until the end of the lease, total money that will be paid out is $1000 x 6 = $6000,

If they leave, they'll have to forgo $1000.

If they move to their new apartment, they'll pay $900 x 6 = $5400

total expenditure if they move to the new place at the end of the six months period will be, the $1000 that will not be refunded back to them on the old apartment, plus this new $5600 for six month's rent in this new apartment, and that will be a total of $6400.

It would be wiser for the couple to stay in the old apartment and save $1400.

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Answer:

56

Step-by-step explanation:

its 56 b

We can conclude that -

An inequality compares two or more numbers or expressions with one another. For example -

2x + 4y > 7

2x + 5y < 6

Given is the table that shows the cost of renting a sound system for a concert. Isabel rents a sound system at 1 p.m. and plans to return it before 4 p.m.

The total number of hours for which she will rent the sound system is -

{h} = 4 - 1 = 3 hours

{h} = 3 hours

Now, for 3 hours, the given inequality is -

2 < x ≤ 3

We can write the cost as $60.

If she is 30 minutes late, then she will pay $72.

Therefore, we can conclude that -

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Answer:

1440

Step-by-step explanation:

theres 144 months in 12 years and I just multiplied it by 10

Answer:

R=V/I

Step-by-step explanation:

Divide V by I to isolate R on one side.

Answer:

R=V/I

Step-by-step explanation:

Because resistance formula is v/i

Answer:

A) a = 25

B) b = 14

Step-by-step explanation:

hopefully this helps :)

Solve the following:

\( \\ \sf \: a) \: \: \frac{a}{5} + 3 = 8\)

\( \\ \sf \: b) \: \: \frac{3b}{7} - 1 = 5\)

Solving question a) :

\( \\ \sf \frac{a}{5 } + 3 = 8\)

\( \\ \sf \mapsto \frac{a + 15}{5} = 8\)

\( \\ \sf \mapsto \: a + 15 = 8 \times 5\)

\( \\ \sf \mapsto \: a = 40 - 15\)

\( \\ \sf \mapsto \: a = 25\)

\( \\ \sf \therefore \: a = 25\)

Solving question b) :

\( \\ \sf \frac{3b}{7} - 1 = 5\)

\( \\ \sf \mapsto \: \frac{3b - 7}{7} = 5 \)

\( \\ \sf \mapsto3b - 7 = 5 \times 7\)

\( \\ \sf \mapsto3b = 35 + 7\)

\( \\ \sf \mapsto \: b = \frac{42}{3} \)

\( \\ \sf \mapsto \: b = 14\)

\( \\ \sf \therefore \: b = 14\)

a = 25

b = 14

After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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The audience of each of the four organizations at the end of that year is found by solving the equations given as :

x = 49 million, y = 22 million, z = 21 million and u = 20 million.

Given that,

Combined audience = 112 million

x + y + z + u = 112 [Equation 1]

Other equations are,

y - z = z - u [Equation 2] ⇒ y + u = 2z

Substituting this in [Equation 1],

x + 3z = 112 [Equation 5]

x - y = 3(y - u) + 21 [Equation 3]

x - y + z - u = 28 [Equation 4]

x - y + y - z = 28

x - z = 28 [Equation 6]

Solving [Equation 5] and [Equation 6],

z = 21 and x = 49

Substituting, Equation 1 becomes,

y + u = 42

From Equation 3,

4y - 3u = 28

Solving these two equations,

u = 20 and y = 22

Hence x = 49 million, y = 22 million, z = 21 million and u = 20 million.

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Answer:

The answer is A

Step-by-step explanation:

I just know

The correct answer is B. $0.25 per pound

8 pounds for oranges costs $2

∴ 1 pound for oranges will cost $ \(\frac{2}{8}\)   =  $ \(\frac{1}{4}\)  

                                                    = $ 0.25

∴ the cost per pound for oranges is $ 0.25

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Answer: 396 inches

Step-by-step explanation:

Let's remember that for every yard there are 36 inches

there are 11 yards total

so we need to multiply 36 by 11

36x11

396 inches

Answer:

396 inches

Step-by-step explanation:

You multiply the number of inches for every yard (36) by the total number of yards

11*36=396

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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The total surface area of the cone is 427.04 square inches.

For a cone of radius R and slant height L, the total surface area is given by the formula:

S = π*R*L + π*R²

Where π = 3.14

In this case, we know that the radius of the cone is 8 inches, and the slant height of the cone is 9 inches.

Then the total surface area of the cone is:

S = 3.14*8in*9in + 3.14*(8in)²

S = 427.04 in²

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Answer:

1 = yes

2 = no

3 = no

4 = yes

5 = yes

6 = no

7 = no

8 = no

0.137606 the standard error of the average amount of coffee a stat 107 student drinks per day is greater than 12.7 oz.

Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Statisticians can assess if the data fits into a normal distribution or another mathematical connection using the standard deviation. The average, or mean, data point will be within one standard deviation of 68% of the data points if the data follow a normal curve.

Given that,

Standard deviation (σ) = 5.2 oz

mean (μ) = 10 oz

Number of students (n) = 120

As we know,

P ( z > 12.7 oz.) = P (z > [{x(avg.) - μ\(\sqrt{n}\)}/σ])

                        = P (z > [{12.7 - 10\(\sqrt{120}\)}/5.2])

                        = P (z > 1.86)

                        = 1 - P ( z < 1.86)

                        = 1 - 0.862394

                        = 0.137606

Thus, P( z > 12.7 oz.) = 0.137606

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Another way to write the compound inequality is 2 ≤ y+3 < 6. The 1st option is the answer

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4

Given: y + 3 ≥ 2 and y + 3 < 6

To write these in another way, change the inequality sign of one of the inequalities by rearranging. That is:

y + 3 ≥ 2 can be rewritten as 2 ≤ y+3. Thus, we have:

2 ≤ y+3 and y + 3 < 6

Combine the two:

2 ≤ y+3 < 6

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Answer:

Let's solve for m.

3m + 4n = 625

Step 1: Add -4n to both sides.

3m + 4n + −4n = 625 + −4n

3m = −4n + 625

Step 2: Divide both sides by 3.

3m/3 = 4n + 625/3

m = -4/3 n + 625/3

C) The variable m in the equation represents the number of hours Amy traveled on the

first train.

D) The variable n in the equation represents the number of hours Amy traveled on the

second train.

Answer:

71°

Explanation

Given the angle m<8 = 109°

Since L || M, hence m<6 = m<8 = 109° (Corresponding angle)

Also the sum of m<5 and m<6 are supplementary, hence;

m<5 + m<6 = 180

Substitute m<6 = 109°

m<5 = 180 - m<6

m<5 =180 - 109

m<5 = 71°

Hence the measure of m<5 is 71°

Answer:

-300

Step-by-step explanation:

because is in the negative and is a number bigger than 23 but in negative.

Answer:

about x=38.1

Step-by-step explanation:

9x38.1=342.9

Answer:

200$ in first year

Step-by-step explanation:

The required expression is (x / 5) + 9

Given that we have to build an equation for the statement "9 more than the quotient of x and 5,

So,

This expression represents the quotient of x divided by 5, and then adding 9 to the result.

Therefore,

"9 more than the quotient of x and 5" can be written mathematically as:

(x / 5) + 9

Hence the required expression is (x / 5) + 9

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Along a 48-mile trail, Alex was biking. He was biking twice as quickly in the first half of the period as in the second. If he drove for four hours, his initial speed would be roughly 16 mph.

An equation is deemed to be linear if the greatest power of the variable is consistently 1. This is also referred to as a one-degree equation.

Given the distance traveled is 48 miles. Let's consider x to be the speed of Alex's bike in the last 2 hours and 2x to be the speed of the same bike in the first 2 hours. Then, the speed of his bike is found by,

\(\begin{aligned}2x(2)+(x)(2)&=48\\4x+2x&=48\\6x&=48\\x&=\frac{48}{6}\\&=8\end{aligned}\)

Then the speed of the bike for the last two hours is 8 mph and the first two hours (2x) is 16 mph.

The complete question is -

Alex was biking along a 48-mile trail. The first half of the time he was biking twice as fast as the second half of the time. If he spent 4 hours on the road, how fast was he biking at first?

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Answer:

d

Step-by-step explanation:

Answer:

Choice B: Start at the origin. Move \(x\) units to the right, and \(y\) units upwards.

Step-by-step explanation:

There are two axes on a typical Cartesian coordinate plane:

Many diagrams of a Cartesian plane would have arrows on these two axis. Typically, there would be:

The arrow on the \(x\)-axis pointing rightward suggests that as a point move to the right, the \(x\!\) coordinate of that point would increase. Conversely, it would be necessary to move points to the right so as to increase their \(\! x\)-coordinates.

On the other hand, the arrow pointing upwards on the \(y\)-axis indicate that as a point move upward, the \(y\!\) coordinate of that point would increase. With a similar logic, it would be necessary to move points upward to increase their \(\! y\)-coordinates.

Besides, the origin (the intersection of the two axis, unless otherwise specified) would corresponds to \((0,\, 0)\). (That is: \(x = 0\) and \(y = 0\).) If the origin \((0,\, 0)\!\) is the starting point, it would be necessary to increase the \(x\)-coordinate by \(x\!\) units (by moving rightward \(x\!\!\) units) and increase the the \(y\)-coordinate by \(y\!\) units (by moving upwards \(y\!\!\) units) so as to reach the point \((x,\, y)\).

Answer:

as all the sides are parallel to each other.

Step-by-step explanation:

the small lines on each side of the kite shows that all sides are equal / parallel to each other.

For the given figure, triangle ADB is congruent to triangle CBD, by SSS postulate.

In congruent geometry, the shapes are so identical that can be superimposed on themselves.

Consider triangle ADB and CDB,
AB = CB  [given]
AD = CD  {given}
BD = BD  [common side]

So, triangle ADB ≅ triangle  CDB, by SSS postulate.

Thus, triangle ADB ≅ triangle  CDB

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The measure of the ∠ RST if, In Δ QRS, QS is extended through point S to point T, a measure of the ∠ QRS = (x + 8)°, m ∠ RST = (4x + 11)°, and m ∠ SQR = (x + 13)°, is 31°.

One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices, known as a triangle.

Given:

In Δ QRS, QS is extended through point S to point T, a measure of the ∠ QRS = (x + 8)°, m ∠ RST = (4x + 11)°, and m ∠ SQR = (x + 13)°,

Calculate the value of x as shown below,

∠ RST = ∠ SQR + ∠ QRS   (Using exterior angle theorem)

4x + 11 = x + 13 + x + 8

4x - x - x = 13 + 8 - 11

2x = 10

x = 5

Calculate the measure of ∠ RST as shown below,

∠ RST = 4 × 5 + 11

∠ RST = 20 + 11

∠ RST = 31°

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