A box of six pencils cost £1.56. A box of eight rubbers cost £2.72. What is the difference in cost between one pencil and one rubber?​

Answer:

The answer is:  −x² + 3x + 2

Step-by-step explanation:

divide the whole expression by -6x

then you get: −x² + 3x + 2

The first five terms of the sequence with a = 3 and r = -2 are: 3, -6, 12, -24, 48.

The general formula for a geometric sequence is given by:

an = a * r^(n-1)

where "a" is the first term, "r" is the common ratio, and "n" is the number of the term we want to find.

In this case, we have:

a = 3

r = -2

So the first term is 3, and the common ratio is -2. We can use the formula above to find the first five terms of the sequence:

a1 = 3

a2 = 3 * (-2)^(2-1) = -6

a3 = 3 * (-2)^(3-1) = 12

a4 = 3 * (-2)^(4-1) = -24

a5 = 3 * (-2)^(5-1) = 48

Therefore, the first five terms of the geometric sequence with a = 3 and r = -2 are: 3, -6, 12, -24, 48.

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Answer:

[tex] \sqrt{98} = \sqrt{49 \times 2} = \sqrt{49} \sqrt{2} = 7 \sqrt{2} [/tex]

Answer: A

Step-by-step explanation:

The answer is A.

Answer:

The height of the prism is 9yd.

Step-by-step explanation:

The volume of the prism is

Vol

= BaseArea×height

The area of the base is the area of the triangle.

Area_triangle

= 1/2 b•h

= 1/2•8•7

= 28

28 is the BaseArea of the prism.

Again the volume of the prism is:

Vol = BaseArea•h

This h is the height of the prism. That is what we are looking for.

Fill in what we know or calculated already.

252 = 28•h

Divide by 28

9 = h

The height of the prism is 9yd.

Answer:

6.1 cm

Step-by-step explanation:

We have to find the hypotenuse of the orange triangle which will be the leg of the green triangle

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]4.2^{2}[/tex] + [tex]4^{2}[/tex] = [tex]c^{2}[/tex]

17.64 + 16 = [tex]c^{2}[/tex]

33.64 = [tex]c^{2}[/tex]

[tex]\sqrt{33.64}[/tex] = [tex]c^{2}[/tex]

5.8 = c

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]2^{2}[/tex] + [tex]5.8^{2}[/tex] = [tex]c^{2}[/tex]

4 + 33.64 = [tex]c^{2}[/tex]

37.64 = [tex]c^{2}[/tex]

[tex]\sqrt{37.64}[/tex] = [tex]\sqrt{c^{2} }[/tex]

6.13514466007 = c  This is a rounded number.  This is an irrational number.  It never repeats or terminates.

Rounded to 1 decimal place

6.1

Helping in the name of Jesus.

Answer:

Step-by-step explanation: Twice means x2

Difference means subtract

A number is a unknown value so you put a variable

(Z - 4) x 2= 7

3.5 x 2= 7

(7.5 - 4) x 2= 7

The 99% confidence interval, zα/2 ≈ 2.576 and for the 94% confidence interval, zα/2 ≈ 1.88.

Hi! To find the zα/2 value for both the 99% and 94% confidence intervals, we will use the standard normal distribution table or a calculator with a z-score function.

For a 99% confidence interval, the area between the two tails (α) is 1 - 0.99 = 0.01. We need to find the value that corresponds to an area of 0.01/2 = 0.005 in each tail. Looking up this value in a standard normal distribution table or using a calculator, we get zα/2 ≈ 2.576.

For a 94% confidence interval, the area between the two tails (α) is 1 - 0.94 = 0.06. We need to find the value that corresponds to an area of 0.06/2 = 0.03 in each tail. Looking up this value in a standard normal distribution table or using a calculator, we get zα/2 ≈ 1.88.
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Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer and Explanation: Nuclear fusion takes place at very high temperature and pressure so that the two elements fuse together, forming new, heavier elements. The nuclear fusion reaction releases a massive amount of energy, and it normally takes place in the core of the stars.

hope that was the answer

Answer:

Its c it has to be because its merge and if u look it up it shows and that's what it means yw!

Step-by-step explanation:

Answer:

Necesito puntos, lo siento, no puedo ayudarlo con la pregunta, solo informe esto y elimínelo o lo que sea

Step-by-step explanation:

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &25 \end{cases} \\\\\\ A = 4000e^{0.08\cdot 25} \implies A=4000e^2\implies A \approx 29556.22[/tex]

The woman will arrive in New York City at 11 AM.

Plane takeoff angle.

Angel

During take off, a plane leaves the ground and travels in a straight line until it reaches a height of 10 km. The distance the plane flies during take off should be in the range 57 km to 62 km. What is the smallest possible angle that the path of the plane could make with the ground? Give your answer in degrees to 1 d. p.

Let's assume that the plane travels a distance of x km during take off and reaches a height of 10 km. Then, using trigonometry, we can find the angle θ between the ground and the path of the plane:

tan(θ) = 10/x

We want to find the smallest possible angle θ, which means we need to maximize x. From the given information, we know that x must be in the range 57 km to 62 km. Therefore, to maximize x, we choose x = 62 km.

Plugging this into the equation above, we get:

tan(θ) = 10/62

θ = arctan(10/62) ≈ 8.8°

Therefore, the smallest possible angle that the path of the plane could make with the ground is approximately 8.8 degrees.

Angel

Xochitl spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7425 feet. Xochitl initially measures an angle of elevation of 19° to the plane at point A. At some later time, she measures an angle of elevation of 37° to the plane at point B.

Find the distance the plane traveled from point A to point B. Round your answer to the nearest foot if necessary

Let's assume that the distance from Xochitl to point A is d1 and the distance from Xochitl to point B is d2. We want to find the distance the plane traveled from point A to point B, which is the difference between d1 and d2.

From the given information, we can set up the following two equations:

tan(19°) = 7425/d1

tan(37°) = 7425/d2

Solving for d1 and d2, we get:

d1 = 7425/tan(19°) ≈ 22977.6 feet

d2 = 7425/tan(37°) ≈ 13060.2 feet

Therefore, the distance the plane traveled from point A to point B is:

d1 - d2 ≈ 9917.4 feet ≈ 3021 meters

Rounding to the nearest foot, we get that the distance the plane traveled from point A to point B is approximately 9917 feet.

Angel

Plane B is flying 75mph 75 ⁢ mph faster than Plane A. Find the time it takes for Plane A to travel 2300 2300 miles if it takes Plane B the same amount of time to travel 2600 2600 miles.

Let's start by using the formula for distance, rate, and time:

distance = rate x time

Let's assume that Plane A's speed is r mph. Then we know that Plane B's speed is r + 75 mph.

We also know that Plane A travels 2300 miles and Plane B travels 2600 miles. Since they take the same amount of time to travel their respective distances, we can set up the following equation:

2300/r = 2600/(r + 75)

To solve for r, we can cross-multiply and simplify:

2300(r + 75) = 2600r

2300r + 172500 = 2600r

300r = 172500

r = 575 mph

Now that we know Plane A's speed, we can use the formula for distance, rate, and time to find the time it takes for Plane A to travel 2300 miles:

distance = rate x time

2300 = 575 x time

time = 4 hours

Therefore, it takes Plane A 4 hours to travel 2300 miles.

Angel

A woman leaves at 7 AM and drive to New York City 200 miles away. If she averages 50 mph what time will she arrive at the city?

To determine the arrival time of the woman in New York City, we need to use the formula for time:

time = distance / rate

In this case, the distance is 200 miles and the rate (or speed) is 50 mph. Plugging these values into the formula, we get:

time = 200 miles / 50 mph = 4 hours

Since the woman left at 7 AM, we can simply add the travel time of 4 hours to the departure time to get the arrival time:

7 AM + 4 hours = 11 AM

Therefore, the woman will arrive in New York City at 11 AM.

Answer:

34833,33 £

Step-by-step explanation:

First, we need to find how much will her sallary increase:

[tex] \frac{28500 \times 2}{9}≈ 6333.33[/tex]

And now we add this number to her old salary:

28500 + 6333,33 = 34833,33 £

Answer:

0.337 or about 33.7%

Step-by-step explanation:

The number of ways to choose 1 apple out of 9 is:

C(9, 1) = 9! / (1! * (9 - 1)!) = 9

The number of ways to choose 2 oranges out of 7 is:

C(7, 2) = 7! / (2! * (7 - 2)!) = 21

So the total number of ways to choose 1 apple and 2 oranges is:

9 * 21 = 189

The total number of ways to choose 3 fruits out of 16 is:

C(16, 3) = 560

Therefore, the probability of selecting 1 apple and 2 oranges is:

189 / 560 ≈ 0.337 or about 33.7%

Answer: 2.86 (2 d.p.)

Step-by-step explanation:

The formula for the circumference of a circle is C = πd = 2πr

Substitute 18 for C in the equation

18 = 2πr

Rarrange for r

r = 18 / 2π = 2.86 (2 d.p.)

Answer:

infinite number of solutions

Step-by-step explanation:

y = x - 8 → (1)

2x - 2y = 16 → (2)

substitute y = x - 8 into (2)

2x - 2(x - 8) = 16

2x - 2x + 16 = 16 ( subtract 16 from both sides )

0 = 0 ← true statement

this true statement indicates the system has an infinite number of solutions

There are 210 ways that Janelle can choose 4 colors from 10 available colors for her art project.

Janelle needs to choose 4 colors out of 10 available colors for her art project. The order in which she chooses the colors does not matter. We can use the combination formula to determine the number of ways she can choose 4 colors from 10 available colors:

nCr = n! / r!(n - r)!

where n is the total number of colors available, r is the number of colors Janelle needs to choose, and ! denotes the factorial operation.

In this case, we have:

n = 10 (total number of colors available)

r = 4 (number of colors Janelle needs to choose)

Substituting these values into the formula, we get:

10C4 = 10! / 4!(10 - 4)!

= 10! / 4!6!

= (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1)

= 210

Therefore, for her art assignment, Janelle can select 4 colors from a palette of 10 in 210 different ways.

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Answer:

180

Step-by-step explanation:

3x10= 30

30/5 = 6

30 x 6 = 180

Answer: 4424.4 pesos

Step-by-step explanation:

To convert dollars to pesos, we need to multiply the number of dollars by the exchange rate:

360 dollars x 12.29 pesos/dollar = 4424.4 pesos

Therefore, Todd will get 4424.4 pesos for his trip to Mexico.

Therefore, the volume of the cone to the nearest cubic meter is approximately 333 cubic meters.

Volume is a measure of the quantum of three- dimensional space enthralled by an object, substance, or region of space. It's frequently measured in boxy units similar as boxy measures, boxy bases, or liters. The volume of an object can be calculated using its confines similar as length, range, and height, or by relegation styles where the volume of the object is determined by the quantum of fluid it displaces when submerged in a liquid. The conception of volume is used in numerous areas of wisdom, engineering, and everyday life, similar as measuring the capacity of holders, determining the quantum of fluid in a force, or calculating the size of a room.

by the question.

To find the volume of a cone, we can use the formula:

[tex]V = (1/3) * π * r^2 * h[/tex]

where V is the volume, r is the radius, and h is the height.

Plugging in the given values, we get:

[tex]V = (1/3) * π * (meters)^2 * (meters)[/tex]

V ≈ 333.33 cubic meters (rounded to the nearest cubic meter)

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Answer: First, we need to calculate the taxable income, which is the gross salary minus the tax-free threshold of $18,200:

Taxable income = Gross salary - Tax-free threshold

Taxable income = $18,700 - $18,200

Taxable income = $500

Since the taxable income falls within the range of $18,201-$37,000, we can use the tax rate of 19c for each $1 over $18,200 to calculate the amount of tax payable:

Tax on income = (Taxable income - $18,200) × 0.19

Tax on income = ($500 - $18,200) × 0.19

Tax on income = -$3,382 × 0.19

Tax on income = -$642.58 (rounded to the nearest cent)

However, the calculated tax is negative, which means that the person is entitled to a tax refund as they have paid more tax than they are required to. This can happen if they have been working for only part of the financial year, or if they have had tax withheld at a higher rate than necessary.

Step-by-step explanation:

Answer:

5cm because you have to round off to the nearest 1000

The cοrrect answer is x > 0 and x < (- 3) where x is any number οn the number line.

A number line is a οne dimensiοnal graph (rather an endless straight line) οn which οne can represent every pοssible real number. Usually we have zerο serving as the center οf the number line, with the right hand side serving as the pοsitive part οf the real line and the left hand side as the negative part οf the real line.

A number line is endless which implies there is nο bοund tο a number line.

Any number οn the real line is denοted by a dark spοt οn the real line. Fοr example if οne needs tο denοte 3 οn the real line he/she has tο mark 3 with a spοt.

There are three kind οf intervals that can be represented οn the number line namely clοsed [ ] , οpen ( ) and semi-clοsed οr semi- οpen [ ) οr ( ]. Intervals οn number line are being shοwn by thickening that part οf the real line that are under cοnsideratiοn.

Fοr example: (4 , 5) is representing by thickening the number line between 4 and 5 with οpen ends , i.e. circles οn digit 4 and 5.

[4 , 6]   is represented by thickening the number line between 4 and 6 with clοsed οr black dοt ends.

Similarly semi οpen and semi clοsed intervals are represented by thickening the interval between thοse twο pοints with apprοpriate circles and dοts οn the endpοints.

Accοrding tο the given questiοn we need tο mark all described pοints that are pοsitive. Thus all pοints greater than zerο are tο be thickened (excluding zerο). This is dοne by having an οpen end οn pοint zerο and thickening the whοle οf the right hand side οr the pοsitive side οf the number line.

Similarly tο represent all described pοints οn the number line less than ( -3) (excluding ( - 3)) can be dοne by having an οpen end οn pοint ( - 3) and thickening the whοle οf the negative side tο the left οf ( - 3).

Thus to represent all the required points we can write them in a set A as:

A = { x : x > 0; x < ( - 3) }.

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Answer:

Michael needs to purchase 6 1/4 feet of metal flashing.

Step-by-step explanation:

To determine the number of feet of metal flashing that Michael needs to purchase, we need to add the lengths of the two small pieces he already has:

3 1/8 feet + 1 3/4 feet

To add these two fractions, we need to have a common denominator. In this case, the smallest common denominator is 8:

3 4/8 feet + 1 14/8 feet = 4 18/8 feet

Now we can simplify the mixed number by converting it to an improper fraction:

4 18/8 feet = (4 x 8 + 18)/8 feet = 50/8 feet

So Michael already has 50/8 feet of metal flashing. To determine how much more he needs to purchase, we need to subtract this amount from the total amount he needs:

6 1/2 feet - 50/8 feet

To subtract these two fractions, we again need to have a common denominator. In this case, the smallest common denominator is 8:

6 4/8 feet - 50/8 feet = (6 x 8 + 4)/8 feet - 50/8 feet = 52/8 feet - 50/8 feet = 2/8 feet

So Michael needs to purchase an additional 2/8 feet of metal flashing to complete his household project, which simplifies to 1/4 feet. Therefore, Michael needs to purchase a total of:

50/8 feet + 1/4 feet = 6 1/4 feet

the probability that a randomly selected light bulb will last between 675 and 825 hours is 68.26%, or 0.6826.

Probability is a measure of the likelihood of an event occurring. It is a numerical value that ranges from 0 to 1, where 0 represents an impossible event and 1 represents a certain event. A probability of 0.5 (or 50%) means that the event is equally likely to occur as not occur.

To solve this problem, we can use the standard normal distribution with a mean of 0 and a standard deviation of 1, and then convert the given values to z-scores using the formula:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

For the lower value of x (675 hours), the z-score is:

z = (675 - 750) / 75 = -1

For the upper value of x (825 hours), the z-score is:

z = (825 - 750) / 75 = 1

We can then use a standard normal distribution table or calculator to find the probabilities associated with these z-scores:

P(z < -1) ≈ 0.1587

P(z < 1) ≈ 0.8413

The probability of a randomly selected light bulb lasting between 675 and 825 hours is then:

P(-1 < z < 1) = P(z < 1) - P(z < -1) ≈ 0.8413 - 0.1587 ≈ 0.6826

Therefore, the probability that a randomly selected light bulb will last between 675 and 825 hours is approximately 68.26%, or 0.6826 as a decimal.

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The complete question is:

Image is attached below.

a. The probability that both of them are good is 9/16

b. Probability that one battery is good while one 3/16

c. probability that both batteries are bad is 1/16

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1.

Probability = sample space / total outcome

the sample space for bad batteries = 5

the sample space for good batteries = 15

Therefore

a. probability that both are good = 15/20 × 15/20 = 3/4 × 3/4 = 9/16

b. probability that a battery is good and the other is bad = 15/20 × 5/20

= 3/4 × 1/4 = 3/16

c. The probability that both are bad

= 5/20 × 5/20 = 1/4 × 1/4 = 1/16

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Rectangle ABCD has diagonals AC and BD that converge at point O and

OA = 5x-7, OD = 4x-5.

A relation is any subset of a Cartesian product.

As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."

A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.

Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).

A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).

Every function, as you can see from these definitions, is a relation from X

Hence, Rectangle ABCD has diagonals AC and BD that converge at point O and

OA = 5x-7, OD = 4x-5.

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I HOPE THIS HELPS

x=−7

x=−1

x

2

=−8x−7

Add 8x to both sides.

x

2

+8x=−7

Add 7 to both sides.

x

2

+8x+7=0

To solve the equation, factor x

2

+8x+7 using formula x

2

+(a+b)x+ab=(x+a)(x+b). To find a and b, set up a system to be solved.

a+b=8

ab=7

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. The only such pair is the system solution.

a=1

b=7

Rewrite factored expression (x+a)(x+b) using the obtained values.

(x+1)(x+7)

To find equation solutions, solve x+1=0 and x+7=0.

x=−1

x=−7