In a sale, normal prices are reduced by 25%. Freddie bought a car in the sale. The sale price of the car was £7500. Work out the normal price of the car.

The number of total different outcomes are, 7,776.

What is rolling dice?

Every face of a cube known as a dice has a unique number.

By throwing a dice into the air, players can advance in any game by getting a certain number. Typically, this dice or dice has numbers from 1 to 6 written on each face or side of the cube-like shape.

Given:

Discrete 5 dice of different colors are rolled, and the number coming up on each dice is recorded.

Since all the dice are of different colors.

So any combination of the numbers on the dice is unique.

Dice has numbers 1 to 6.

So, for each dice there are 6 possibilities.

Since number coming on a dice is independent to the number coming on the another dice.

So, total different outcomes are = 6 x 6 x 6 x 6 x 6 = 6^5 = 7776.

Hence, the number of total different outcomes are, 7,776.

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Step-by-step explanation:

this is the answer bro or sis.

Answer:

cashier

Step-by-step explanation:

the discount is $7.50

Answer: C 1/4

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

edge 2021

Answer:

I don't know!

Step-by-step explanation:

Answer:

Step four

Step-by-step explanation:

When solving equations you have to flip the sign when you divide negative integers.

Answer:

from my observation there is no mistake but here is my solution

Step-by-step explanation:

-2n+6-5>9

-2n+1>9

-2n>9-1

-2n>8

divide both sides by-2

n>-4

Answer: 2/6 or 1/3

Step-by-step explanation:

SCHOOL has 6 letters in it and two O's. Therefore, it would be 2/6 or simplified it would be 1/3.

That was FUN!

For the 1st one, the equations never intersect. There is only 1 case where the lines never intersect and that is when they are parallel. So the 1st one is that they are parallel. A and B are parallel when graphed.

For the 2nd one, the lines are always intersecting. This means that C and D are the same line when graphed.

Answer:

see explanation

Step-by-step explanation:

The solution of equations given graphically is at the point of intersection of the 2 lines.

No solution indicates that there is no point of intersection, thus the graph of A and B are parallel lines which never intersect.

B

Infinitely many solutions indicates that the graph of C and D lie on the same line.

Here, we want to find the circumfrence and area of the circle

To find either of this, we need the value of the radius of the circle

The radius of a circle is the distance btetween the center of the circle and the circumfrence of the circle. In this question, this distance is 20 ft

Mathematically, we can calculate the area with the formula;

To calculate the circumfrence of the circle, we use the formula below;

The phasor form of a sinusoid represents the amplitude and phase angle of the sinusoid in complex number notation. In this case, the phasor form of \(8 sin(20t 57)\) would be 8 ∠57°. The amplitude, 8, is the magnitude of the complex number, and the phase angle, 57°, is the angle of the complex number in the complex plane.

In terms of amplitude and phase angle, a sinusoidal waveform is mathematically represented in phasor form. Electrical engineering frequently employs it to depict AC (alternating current) circuits and signals. A complex number that depicts the magnitude and phase of a sinusoidal waveform is called a phasor. The phase angle is represented by the imaginary component of the phasor, whereas the real part of the phasor represents the waveform's amplitude. Complex algebra can be used to analyse AC circuits using the phasor form, which makes computations simpler and makes it simpler to see how the circuit behaves.

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Answer:

Use the quotient property of logarithms, logb(x)−logb(y)=logb(xy) log b ( x ) - log b ( y ) = log b ( x y ) . log3(4010) log 3 ( 40 10 ). Step 2.

Answer:

x=3/5

Step-by-step explanation:

3x+5=0

3x=-5

x=-5/3

Answer:

x = 5/3

Step-by-step explanation:

Given equation: 3x-5 = 0

Add both sides by 5, we get

= 3x - 5 + 5 = 0 + 5

= 3x = 5

Divide both sides by 3, we get

3x/3 = 5/3

or, 3x = 5

so, x = 5/3

Answer:

1. 9

2. -3

Step-by-step explanation:

The graph of the parent absolute value function is decreasing over the interval (-∞, 0). The function exhibits a decreasing behavior as x moves from negative infinity towards zero, where the absolute value decreases.

The parent absolute value function is defined as f(x) = |x|. To determine where the graph of this function is decreasing, we need to identify the intervals where the function's slope is negative.

Let's analyze the behavior of the parent absolute value function:

For x < 0, the function can be rewritten as f(x) = -x. In this interval, the function is a linear function with a negative slope of -1. As x decreases, f(x) also decreases, indicating a decreasing behavior.

For x > 0, the function remains f(x) = x. In this interval, the function is a linear function with a positive slope of 1. As x increases, f(x) also increases, indicating an increasing behavior.

At x = 0, the function is not differentiable since the slope changes abruptly from negative to positive. However, it is worth noting that the function does not strictly decrease or increase at x = 0.

Therefore, we can conclude that the graph of the parent absolute value function is decreasing over the interval (-∞, 0).

In this interval, as x moves from negative infinity towards zero, the function values decrease. The farther away x is from zero (in the negative direction), the larger the absolute value, resulting in a decrease in the function values.

On the other hand, the graph of the parent absolute value function is increasing over the interval (0, ∞), as explained earlier.

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Answer:

check book

Step-by-step explanation:

ok apply formula only

To calculate the moment of inertia about the x-axis, the moment of inertia about the y-axis, and the polar moment of inertia passing through point O, we need to determine the geometric properties of the given figure, such as the shape and dimensions.

To calculate the moment of inertia about the x-axis, we need to determine the area of the figure and the distance of each element from the x-axis. The moment of inertia about the x-axis, denoted as Ix, is given by the sum of the individual moments of inertia of each element about the x-axis.

Similarly, to calculate the moment of inertia about the y-axis (Iy), we need to determine the area of the figure and the distance of each element from the y-axis. The moment of inertia about the y-axis is given by the sum of the individual moments of inertia of each element about the y-axis.

The polar moment of inertia passing through point O (J) represents the resistance of the entire figure to torsional or rotational deformation. It is the sum of the moments of inertia about the x-axis and y-axis, denoted as Ix and Iy, respectively.

The specific calculation method will depend on the shape and dimensions of the figure. For example, if the figure is a rectangle, the formulas for calculating the moments of inertia and the polar moment of inertia can be found in engineering mechanics or solid mechanics textbooks.

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Answer: A.

\(H_0:p=0.12\\\\H_a:p<0.12\)

Step-by-step explanation:

Null hypothesis\((H_0)\) : A statement describing population parameters as per the objective of the study. It usually takes "≤,≥,=" signs.  

Alternative hypothesis \((H_a)\): A statement describing population parameters as per the objective of the study. It usually takes ">, <, ≠" signs.

Let p be the proportion of screens that will be rejected.

12 percent of the screens manufactured using a previous process were rejected at the final inspection.

(i.e. p= 0.12)

Objective of the study = whether the new process reduces the population proportion of screens that will be rejected

i.e. p< 0.12

So, the appropriate hypotheses to investigate whether the new process reduces the population proportion of screens that will be rejected:

\(H_0:p=0.12\\\\H_a:p<0.12\)

To determine which differential equation(s) are linear, we need to examine the form of each equation. A linear differential equation is one that can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x), b(x), c(x), and g(x) are functions of x.

The differential equation 2xy" - 5xy' + y = sin(3x) is linear. It can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x) = 2x, b(x) = -5x, c(x) = 1, and g(x) = sin(3x).
The differential equation (v)² + xy = In(x) is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (v)², where v represents the derivative of y with respect to x. This term does not have a linear coefficient.
The differential equation y' + sin(y) = e^(3x) is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = sin(y), and g(x) = e^(3x).
The differential equation (x²+1)y" - 3y - 2x³y = -x - 9 is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (x²+1)y", where the coefficient is a function of x.
The differential equation y' + xy = y" is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = x, and g(x) = y".

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Answer: The trapezoid's area is 265 \(unit^{2}\)

Definition of a trapezoid - A trapezoid, also known as a trapezium, is a flat closed shape having four straight sides, with one pair of parallel sides.

The parallel sides of a trapezium are known as the bases, and its non-parallel sides are called legs. A trapezium can also have parallel legs. The parallel sides can be horizontal, vertical, or slanting.

The perpendicular distance between the parallel sides is called the altitude.

The area of trapezium is given as : \(\frac{1}{2}\) × sum of the parallel sides × distance between the parallel sides

Given:  the base lengths of trapezoid are 24 unit and 29 unit and height is 10 unit.

The area of trapezoid = \(\frac{1}{2}\) × (24+29) × 10 = 265 \(unit^{2}\)

Final answer : The area of trapezoid is 265\(unit^{2}\)

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The area of the shaded region found using trigonometric ratios is about 86.6 square centimeters

Trigonometric ratios are expressions of the relationship between the interior angle of a right triangle and the ratio of two of the sides of the triangle.

Whereby, the inscribing figure of the quadrilateral is a regular hexagon, we get;

Interior angle of a regular hexagon = 120°

The 10 cm segment bisects the top vertex angle of the regular hexagon, which together with the 5·√3 cm side and trigonometric ratios, indicates that we get;

sin(60) = s/(5·√3) = (√3)/2

Where;

s = The side length of the regular hexagon

(5·√3)/s = (√3)/2

s = (5·√3)/((√3)/2) = 10

The side length of the regular hexagon, s = 10

The area of the regular hexagon, A = ((3·√3)/2) × s² = (1/2)×6 ×s ×a

Where;

a = The apothem = 5·√3

Therefore; A = ((3·√3)/2) × 10² = 150·√3

A  = (1/2)×6 ×10 × 5·√3 = 150·√3

Area of the quadrilateral = 4 × (1/2) × 5·√3 × 10 = 100·√3

Area of the shaded region = Area of the hexagon - Area of the quadrilateral

Therefore;

Area of the shaded region = 150·√3 - 100·√3 = 50·√3 ≈ 86.6

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Answer:

8.9r + (5s + 10)

actually the parenthesis aren't necessary...

8.9r + 5s + 10

Step-by-step explanation:

You can change a subtraction to addition if you change the second term to the opposite sign. This problem is like advanced mode of "Add the Opposite"

8.9r - (-5s - 10)

= 8.9r + (+5s + 10)

= 8.9r + (5s + 10)

= 8.9r + 5s + 10

Answer:

A) x = 15

Step-by-step explanation:

4x - 30 = 2x

subtract 2x from each side of the equation:

2x - 30 = 0

add 30 to each side:

2x = 30

x = 15

Answer:

\( \displaystyle A) {15}^{ \circ} \)

Step-by-step explanation:

remember that,

when a transversal crosses two parallel lines then the Alternate interior angles are equal that is being said

\( \displaystyle 4x - 30 = 2x\)

cancel 2x from both sides:

\( \displaystyle 2x - 30 = 0\)

add 30° to both sides:

\( \displaystyle 2x = 30\)

divide both sides by 2:

\( \displaystyle x =15\)

hence

our answer is A)

Based on this information, we can conclude that the order of simulations from the least sample size (n) to the greatest sample size (n) is:
C) Simulation B, simulation A, simulation C

Based on the given information, we can determine the order of simulations from the least sample size (n) to the greatest sample size (n) by examining the histograms.

Looking at the histograms, we can see that the relative frequencies for each simulation are centered around the population proportion of 0.70.

However, we need to consider the relative frequencies that are closest to 0.70, as they indicate the simulations with sample sizes closest to the population size.

Comparing the histograms, we can see that the relative frequency closest to 0.70 in Simulation A is 0.69. In Simulation C, the relative frequency closest to 0.70 is also 0.70.

However, in Simulation B, the relative frequency closest to 0.70 is 0.80.

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Answer: 2

Step-by-step explanation:

yeah

Answer:

345.6

Or 345 full cubes

Step-by-step explanation:

To answer this question we first need to find the volume of the cuboid!

To find volume we use the equation...

For the cuboid we are given the dimensions 60, 24 and 30 so we just need to multiply them...

We now need to the the volume of the cube which we can just do by cubing the value given

We now need to divide the two results together to find out how many cubes would fit...

Hope this helps, have a lovely day!

Answer:

The answer would be P(x) = 1573*(1.02)^x

Using the normal distribution, the probability that the sample proportion of households spending more than $125 a week is less than 0.3 is 30.29%.

Normal distribution refers to a continuous probability distribution wherein values lie in a symmetrical fashion mostly centered around the mean. In a normal distribution, the probability is calculated using the z-score of a measure X. A Z-score refers to a numerical measurement that defines a value's relationship to the mean (of a group of values).

In order to determine the probability of the sample proportion, the z-score of a measure X is determined.

z-score = (X - µ)/σ where µ is the mean and σ is the standard deviation.

The standard deviation σ = √(p(1-p)/n

From the given data:

n = no of random sample = 145

p = probability of success (household spending more than $125) = 0.32

Hence,

σ = √((0.32(1-0.32)/145) = 0.0387

Calculating the z-score when X = 0.3

z-score = (0.3 – 0.32)/0.0387 = -0.516

From the table, the probability of z = -0.516

P(X<z) = 0.30293 or 30.29%

The probability that the sample proportion of households spending more than $125 a week is less than 0.3 is 30.29%.

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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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1. the mean (E(X)) of the random loss amount prior to the deductible is  62.5

2. the variance \((Var(Y^L))\) of the insurance payment per loss is:

\(Var(Y^L)\) ≈ 1584.1875

3.  the mean \((E(Y^P))\) of the insurance payment per payment is approximately 45.36, and the variance \((Var(Y^P))\) is approximately 1965.071.

To calculate the mean and variance of the random loss amount prior to the application of the deductible, we need to consider the probability density function (PDF) provided.

1. Mean and Variance of Random Loss Amount (X) prior to the Deductible:

The PDF is defined as:

f(x) = 0.008,     0 < x ≤ 75

      0.016,    75 < x < 100

The mean (E(X)) is calculated as follows:

E(X) = ∫[x * f(x)] dx

For 0 < x ≤ 75:

E(X) = ∫[x * 0.008] dx

    = 0.008 * [x² / 2] | from 0 to 75

    = 0.008 * [(75² / 2) - (0² / 2)]

    = 0.008 * (5625 / 2)

    = 0.008 * 2812.5

    = 22.5

For 75 < x < 100:

E(X) = ∫[x * 0.016] dx

    = 0.016 * [x² / 2] | from 75 to 100

    = 0.016 * [(100² / 2) - (75² / 2)]

    = 0.016 * (5000 / 2)

    = 0.016 * 2500

    = 40

Therefore, the mean (E(X)) of the random loss amount prior to the deductible is:

E(X) = 22.5 + 40

    = 62.5

The variance (Var(X)) is calculated as follows:

Var(X) = ∫[(x - E(X))²* f(x)] dx

For 0 < x ≤ 75:

Var(X) = ∫[(x - 22.5)² * 0.008] dx

      = 0.008 * [(x - 22.5)³ / 3] | from 0 to 75

      = 0.008 * [(75 - 22.5)³ / 3]

      = 0.008 * [(52.5)³ / 3]

      ≈ 432.1875

For 75 < x < 100:

Var(X) = ∫[(x - 40)² * 0.016] dx

      = 0.016 * [(x - 40)³ / 3] | from 75 to 100

      = 0.016 * [(100 - 40)³ / 3]

      = 0.016 * [(60)³ / 3]

      = 1152

Therefore, the variance (Var(X)) of the random loss amount prior to the deductible is:

Var(X) = 432.1875 + 1152

      ≈ 1584.1875

2. Mean and Variance of Insurance Payment per Loss \((Y^L)\):

The insurance payment per loss is calculated as follows:

\(Y^L\) = X - 40 (deductible)

The mean \((E(Y^L))\) of the insurance payment per loss is:

\(E(Y^L)\) = E(X - 40)

      = E(X) - 40

      = 62.5 - 40

      = 22.5

The variance \((Var(Y^L))\) of the insurance payment per loss is equal to the variance of X since the deductible does not affect the variance.

Therefore, the variance \((Var(Y^L))\) of the insurance payment per loss is:

\(Var(Y^L)\) ≈ 1584.1875

3. Mean and Variance of Insurance Payment per Payment \((Y^P)\):

The insurance payment per payment is equal to the insurance payment per loss \((Y^L)\) when there is a loss (X) and 0 otherwise.

The mean \((E(Y^P))\) of the insurance payment per payment is equal to the probability of a loss multiplied by the mean payment per loss:

\(E(Y^P) = P(X > 40) * E(Y^L)\)

For 0 < x ≤ 75:

P(X > 40) = ∫[f(x)] dx | from 40 to 75

         = 0.008 * (75 - 40)

         = 0.28

For 75 < x < 100:

P(X > 40) = ∫[f(x)] dx | from 40 to 100

         = 0.016 * (100 - 40)

         = 0.96

\(E(Y^P)\) = (0.28 * 22.5) + (0.96 * 22.5)

      ≈ 23.76 + 21.6

      ≈ 45.36

The variance \((Var(Y^P))\) of the insurance payment per payment is equal to the variance of \(Y^L\) multiplied by the probability of a loss:

\(Var(Y^P) = P(X > 40) * Var(Y^L)\)

Var(Y^P) = (0.28 * 1584.1875) + (0.96 * 1584.1875)

        ≈ 444.372 + 1520.699

        ≈ 1965.071

Therefore, the mean \((E(Y^P))\) of the insurance payment per payment is approximately 45.36, and the variance \((Var(Y^P))\) is approximately 1965.071.

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