What strategy could you use to figure out when Beau is likely to win 500 trophies

Answer:

The first discount of 50% means Jason paid 50/100 x £88 = £44 for the jacket.

Then, the second discount of 25% means he paid 75/100 x £44 = £33 for the jacket.

Therefore, the final sale price that Jason paid for the jacket was £33.

Step-by-step explanation:

The expression you provided involves taking the square root of a negative number, which results in an imaginary number. In standard real number arithmetic, the square root of a negative number is undefined. However, in the realm of complex numbers, we can define a square root of negative numbers using the imaginary unit "i," where i is defined as the square root of -1.

Let's break down the expression step by step:

√(-25) / √9

The square root of -25 can be written as √(-1 * 25), which can further be simplified as √(-1) * √25.

√(-1) is equal to "i," and the square root of 25 is 5.

So, the expression becomes:

i * 5 / √9

The square root of 9 is 3.

Now, we can simplify further:

i * 5 / 3

Thus, the simplified expression is (5i) / 3, where "i" represents the imaginary unit.

The surface area of the square Pyramid with a side length of 2 yards and a slant height of 2 yards is 12 square yards.

The surface area of a square pyramid, we need to calculate the area of each face and then sum them up.

A square pyramid has four triangular faces and one square base. The area of the base is equal to the side length squared, while the area of each triangular face can be found using the formula: (1/2) * base * height.

Given that the side length of the square pyramid is 2 yards and the slant height is also 2 yards, we can calculate the surface area as follows:

Area of the base = (side length)^2 = 2^2 = 4 square yards

Area of each triangular face = (1/2) * base * height = (1/2) * 2 * 2 = 2 square yards

Now, let's calculate the total surface area of the square pyramid:

Total surface area = Area of the base + 4 * Area of each triangular face

Total surface area = 4 + 4 * 2 = 4 + 8 = 12 square yards

Therefore, the surface area of the square pyramid with a side length of 2 yards and a slant height of 2 yards is 12 square yards.

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Answer:

R = 2414 units

0.794

Step-by-step explanation:

Given:

Weekly demand, D = 331 units

Lead time (L)= 6 weeks

Standard Deviation (SD) = 85 units

The reorder point is calculated using the relation :

R = D*L + z*(SDw)

SDw = the standard deviation with lead time of 6 weeks ; √6 * 85 = 208.21

z = NORMSINV(0.98) = 2.05

R = (331 * 6) + (2.05 * 208.21)

R = 1986 + 428.122

R = 2414.122

R = 2414 units

The Safety stock, SS

SS = z * SDw

SS = 2.05 * 208.21

SS = 426.8305 units

60% reduction :

426.8305 * (1 - 60%)

= 170.7322

= 171 units

The new service probability ;

SS = z * SDw

171 = z * 208.21

z = 171 / 208.21

z = 0.82

P(Z < 1.02) = 0.7938 = 0.794 = 79.4%

Answer:

9669

Step-by-step explanation:

69

Answer:

1/8*1/3^3

1/8*1/27

1/216

Step-by-step explanation:

just bring 3^-3 down then it will be positive.when u do so it will be1/3^3 .

Answer:

125

Step-by-step explanation:

Sum of Exterior Angles must add to 360 so

\(60 + 70 + 40 + 65 + x = 360\)

\(235 + x = 360\)

\(x = 125\)

Answer:

6

Step-by-step explanation:

Before solve this you've to know that,

( + ) × ( - ) = ( - )

( + ) × ( + ) = ( + )

( - ) × ( - ) = ( + )

Let us solve now.

13 + (-7)

13 - 7

= 6

Hope this helps you :-)

Let me know if you have any other questions  :-)

Answer:

\(6\)

..........

..

The question supplied is incomplete :

The x parameters aren't given ; "Units with weights less than or greater than ounces will be classified as defects"

Assume the unit weights Given are ;

Units with weights less than 10.8 or greater than 11.2 ounces will be classified as defects

Just follow the procedure in the solution for any value of unit weight interval given.

Answer:

0.3173

Step-by-step explanation:

Mean weight, m = 11 ounces

Standard deviation, s = 0.2 ounces

Find the Zscore for each unit weight :

Z = (x - mean) / standard deviation

P(x < 10.8) :

Z = (10.8 - 11) / 0.2 = - 1

P(Z < - 1) = 0.15866

P(x > 11.2) :

Z = (11.2 - 11) / 0.2 = 1

P(Z > 1) = 0.84134

P(x < 11.2) - P(x < 10.8) = 1 - (P(Z < 1) - P(Z < - 1)) = 1 - 1 - (0.84134 - 0.15866) = 1 - 0.68268 = 0.31732

Hence, Probability of a defect is 0.3173

Answer:

7,620,650

Step-by-step explanation:

___________

Answer:

7,620,650

Step-by-step explanation:

To write in standard form, you just write the entire number out.

Answer:

perpendicular.

Step-by-step explanation:

1. common view of slope-interception form is:

y=slope*x+interception;

2. according to the common form slope1*slope2=(-1)*1=-1, then the given lines are perpendicular.

========================================================

Explanation:

a = speed of airplane without any wind

a+50 = speed of the plane with the wind boosting it

distance = rate*time

d = r*t

d = (a+50)*4

This represents the plane traveling 4 hours at the speed of a+50 mph. We don't really care about the distance d.

The other equation to set up is

d = (a-50)*5

which means the plane is going slower at a-50 mph and travels for 5 hours this time.

The system of equations is

\(\begin{cases}d = (a+50)*4\\d = (a-50)*5\end{cases}\)

Both equations involve the same variables 'a' and d, which allows us to use substitution to solve for 'a' like so

d = (a+50)*4

(a-50)*5 = (a+50)*4

5a-250 = 4a+200

5a-4a = 200+250

a = 450

The speed of the plane, without any wind, is 450 mph

Using a calculator, the trigonometric ratio of sin 98 is approximately 0.9848.

One of the trigonometric ratio we have in mathematics is the sine ratio. We can use calculator to find the sine of an angle without making use of tables. To do this on your calculator, enter the sine function followed by the degree of the angle you want to find its sine. You will get your answer.

Using a calculator, we can find the sine of 98 degrees as follows:

sin 98° ≈ 0.9848

Rounding this to four decimal places, we get:

sin 98° ≈ 0.9848

Therefore, sin 98° is approximately equal to 0.9848.

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The actual air temperature is -34.16°.

It should be noted that from the information z the equation that's given was:

y=-16+1.2x

This shows the relationship between the actual air temperature and the temperature.

Therefore, when y is given as -25, the actual air temperature will be:

y=-16+1.2x

-25 = 16 + 1.2x

Collect like terms

1.2x = -25 - 16

1.2x = -41

X = -41/1.2.

x = -34.16

Therefore,the actual air temperature is -34.16°.

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It takes time of near about 35 year.

Given that,

Storage capability of computers has been doubling every 5 years

The date of 1st computer made = 1980

computer could store 5 megabytes,

Now,

We can use the following calculation to determine how long it took computers to store 100 megabytes:

Therefore,

Log₂ (final amount / beginning amount)

=  Log₂ (100 / 0.5)

= log₂ (200)

= 7.64 is the number of doublings.

If each doubling takes five years, then it would take computers just over seven doublings or almost 35 years to store 100 megabytes.

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Answer:

-5/3

Step-by-step explanation:

trust me bro

Answer:

Use desmos

Step-by-step explanation:

Basically it is a graphing calculator put your points

Answer:

483

Step-by-step explanation:

So we have the sequence:

15, 21, 27, 33...

And we want to find the 79th term.

To do so, we can write an explicit formula.

The standard form for an explicit formula for an arithmetic sequence is:

\(x_n=a+d(n-1)\)

Where a is the initial term, d is the common difference, and n is the nth term.

From the sequence, we can see that the initial term a is 15.

We can also see that the common difference is +6. This is because each subsequent term is 6 more than the previous one. 15 plus 6 is 21, 21 plus 6 is 27, and so on.

So, substituting 15 for a and 6 for d yields:

\(x_n=15+6(n-1)\)

To find the 79th term, substitute 79 for n. So:

\(x_{79}=15+6(79-1)\)

Subtract:

\(x_{79}=15+6(78)\)

Multiply:

\(x_{79}=15+468\)

Add:

\(x_{79}=483\)

So, the 79th term is 483.

And we're done!

Step-by-step explanation:

Hey there!

First sequence = 15.

Second sequence = 21.

Their difference = 6.

Now, we have;

\(an = a1 + (n - 1)d\)

Put all values

\(an = 15 + (n - 1)6\)

Simplify it.

\(an = 15 + 6n - 6\)

\(an = 6n + 9\)

Now,

a1 = 6×1+9= 15

a2 = 6×2+9= 21

a3 = 6×3+9= 27.

We have to find 79th term.

a79 = 6×79+9= 483.

Therefore, the 79th term is 483.

Hope it helps...

The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

From the question, we have the following parameters that can be used in our computation:

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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Answer:

1 1/4 miles

Step-by-step explanation:

Check the picture below.

We have:

only 7 digit codes

The number of possible combinations is:

The probability the spy is able to unlock the smart phone on his first try is:

Then:

Answer:

Answer:

\(\sf{x = 2}\)

Step-by-step explanation:

Question type: solving equations with variables on both sides.

\(\textsf{This is a question with variables on both sides, to solve this we need to get the variable x }\)

\(\textsf{alone. (getting the x on one side)}\)

--------------------------------------------------------------

\(\sf{-2x~+~4~=~2x~-~4\)

Subtract 4 from both sides.

\(\sf{-2x~=~2x~-8\)

Subtract 2x from both sides.

\(\sf{-4x~=~-8}\)

Divide both sides by -4.

\(\bf{x~=~2\)

Therefore, x would be 2.

\(-jurii\)

Answer:

x=2

Step-by-step explanation:

The solutions of the equation 3x - y = 1 are (-2,-7),(-1,-4) and (3,8) thus option (A),(B) and (D) are correct.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

In another word, the equation must be constrained with some constraints.

As per the given equation,

3x - y = 1

Substitute, x = -2

3(-2) - y = 1

y = -7 thus  (-2,-7) satisfied.

Similarly (-1,-4) and (3,8) are also satisfied.

Hence "The solutions of the equation 3x - y = 1 are (-2,-7),(-1,-4) and (3,8)".

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Answer:

11.60

Step-by-step explanation:

To find unit rate, you need to use the formula:

(amount of money) ÷ (amount of hours)

Since we have both, we can plug in

140 ÷ 12 will give you approximately 11.6

So, you receive $11.60 every hour.

Answer:

Step-by-step explanation:

The equation of line is y= 6x- 12.

The slope of the line and a point on the line can be used to create the equation of a line. To better comprehend how the equation for a line is formed, let's learn more about the line's slope and the necessary point on the line. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis.

The formula for equation line passes through points

(y\(- y_1\)) = m (x \(-x_1\))

Given:

points (3, 6) and (5, 18)

Now, using equation of line

(y\(- y_1\)) = m (x \(-x_1\))

Now, slope= 18-6/ 5-3

slope= 12/2

slope= 6

Then, equation of line

y- 6 = 6(x - 3)

y-6 = 6x - 18

y= 6x- 12

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The positive square root of 57.27 is approximately 7.5726, with further decimal places available through iterative approximation methods.

To find the positive square root of the number 57.27, we can use a calculator or mathematical operations.

Taking the square root of a number involves finding a value that, when multiplied by itself, gives the original number. In this case, we want to find the value that, when squared, equals 57.27.

Using a calculator, we can find the square root of 57.27 as approximately 7.5726. However, it's important to note that this is an approximation and may not be completely accurate due to rounding errors.

If we want to find a more precise answer manually, we can use iterative approximation methods. One such method is the Newton-Raphson method, which involves repeatedly refining an initial guess.

Starting with an initial guess of, let's say, 7, we can use the formula:

x(n+1) = (x(n) + (57.27/x(n)))/2,

where x(n) is the current approximation and x(n+1) is the next approximation. Iterating this formula a few times will converge to a more accurate value.

After a few iterations, we find that the positive square root of 57.27 is approximately 7.572615. This value can be further refined by performing more iterations or using more advanced numerical methods.

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The inequality that shows how long the temperature in Austin will remain colder than that in San Antonio is 33.5 + 2.5t < 37.5 + 1.5t and the time is less than 4 hours

From the question, we have the following parameters that can be used in our computation:

Austin

Initial temperature = 33.5 degrees Fahrenheit

Rate of increment = 2.5 degrees Fahrenheit

San Antonio

Initial temperature = 37.5 degrees Fahrenheit

Rate of increment = 1.5 degrees Fahrenheit

The above parameters mean that

Current temperature = Initial temperature + Rate of increment x Number of hours

So, we have

Austin: A(t) = 33.5 + 2.5t

San Antonio: B(t) = 37.5 + 1.5t

When Austin is colder than San Antonio, we have

A(t) < B(t)

Substitute the known values in the above equation, so, we have the following representation

33.5 + 2.5t < 37.5 + 1.5t

Evaluate the like terms

t < 4

Divide both sides by 1

t < 4

Hence, the interval is less than 4 hours

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