What fraction of £1 is 31p?

Answer: 6

Step-by-step explanation:

This is a direct application of the exponent rule [tex](a^b)^c=a^{bc}[/tex].

We have to assume that the sample mean is given , distribution is normal and sample size is also given.

Given confidence level 99%.

We have to answer the assumptions that are needed to make a valid 99% confidence interval.

Confidence interval can be made by formula of margin of error.

Margin of error is the difference between actual values and the calculated values.

Upper level of confidence interval=Mean+ margin of error

Lower level of confidence interval= Mean - margin of error.

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where z is the corresponding z value for the confidence level given ,

σ is population mean and n is sample size.

Hence to calculate the confidence interval we need population mean, sample size.

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Answer:

The cost of 30 gallons of gas is $74.7.

Step-by-step explanation:

Step 1 of 3

Here we need to find the cost of 30  gallons.

Given that the price that Tyler pays for gas varies directly with the number of gallons he buys.

The cost of 24  gallons is $59.76  to him.

Let, x  be the number of gallons and y  be the cost or price for gas.

Use the formula for direct variation which is given by y=kx.

Step 2 of 3

Now substitute the value y=$59.76 and x=24.

Put value in y=kx, we get

[tex]$$\begin{aligned}&59.76=k \times 24 \\&k=2.49\end{aligned}$$[/tex]

Substitute value of k is y=kx, we get y=2.49x

Step 3 of 3

Now we need to find the value of y that is the cost for 30 gallons.

Again use direct variation formula y=kx and value of k and x, we get [tex]$y=2.49 \times 30$[/tex]

[tex]$$y=74.7$$[/tex]

The degree of the polynomial is 2

The root of the polynomial is given as:

Root = x - 3i

The above expression is a complex root.

This means that the conjugate is also a root of the polynomial

So, we have

Roots = x - 3i and x + 3i

Multiply the roots

f(x) = (x - 3i)(x + 3i)

This gives

f(x) = x^2 + 9

The degree of the above equation is 2 i.e. the highest power

Hence, the degree of the polynomial is 2

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Answer:

5x/2

Step-by-step explanation:

Say the mystery number is "x"

5 times that = 5 * x = 5x

Then the quotient (that means the result of division, so divide!) of that and 2 would give you: 5x/2

[tex]\angle EHF=90^{\circ}[/tex] (an angle inscribed in a semicircle is a right angle)

[tex]\angle HEF=38^{\circ}[/tex] (alternate segment theorem)

[tex]a=52^{\circ}[/tex] (angles in a triangle add to 180 degrees)

Speedy cage is 2 inches taller than fluffy cage.

The volume of rectangular prism = lwh

where

Therefore,

height of fluffy cage can be calculate as follows:

4340 = 20 × 14 × h

4340 = 280h

h = 4340 / 280

h = 15.5 inches

height of Kenneth cage can be calculate as follows:

5250 = 20 × 15 × h

5250 = 300h

h = 5250 / 300

h = 17.5 inches

height difference = 17.5  - 15.5 = 2.0 inches

Hence, speedy cage is 2 inches taller than fluffy cage.

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The following statements are true:

A negative number in mathematics is any number that is less than zero i.e. x < 0.

This means that zero is greater than any negative number.

However, the higher the digit of a negative number, the smaller that number becomes. It is opposite of positive numbers or integers.

Therefore, the following statements are true:

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Answer:

The function can have its own inverse, that is, [tex]$f^{-1}(x)=f(x)$[/tex] and this type of function is called an involution. Example f(x)=6-x.

Step-by-step explanation:

A statement that a function can be its own inverse is given.

It is required to explain whether a function has its own inverse. Then explain whether the given statement satisfies the condition.

Step 1 of 3

Consider a function is f(x)=6-x.

This function is a continuous function for all values of x. This function is also a linear function. So, every continuous linear function is a one-to-one function.

So, this function is one-to-one.

Step 2 of 3

Consider f(x) as y and rewrite the equation.

The equation becomes [tex]$y=6-x$[/tex]

Solve the rewritten equation.

Add -6 on both sides of the equation.

[tex]$$\begin{aligned}&y=6-x \\&y-6=6-x-6 \\&y-6=-x\end{aligned}$$[/tex]

Step 3 of 3

Multiply by -1 on both sides.

[tex]$$\begin{aligned}&y-6=-x \\&(-1)(y-6)=(-x)(-1) \\&-y+6=x \\&x=6-y\end{aligned}$$[/tex]

Interchange x and y in solved equation.

[tex]$$\begin{aligned}&x=6-y \\&y=6-x\end{aligned}$$[/tex]

So, the inverse of the given function is [tex]$f^{-1}(x)=6-x$[/tex].

The function and inverse of the function are the same, that is, [tex]$f^{-1}(x)=f(x)$[/tex]

So, a function can have its own inverse. This type of function is called an involution.

The points used in plotting the graph of the absolute function as given are; (-2,3), (-1,2), (0,1), (1,0) and (2,1).

The absolute function given is; y = | x − 1 |

Hence, by consider x-values; -2,-1,0,1,2....it follows that the corresponding y-values which are all positive by virtue of the absolute value symbol are; 3, 2, 1, 0, 1.

Hence, the points are; (-2,3), (-1,2), (0,1), (1,0) and (2,1).

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Answer:

(a) 1416

(b) 2 × 2 × 2 × 3 × 59

Step-by-step explanation:

The prime numbers between 0 and 10 are 2, 3, 5,7 (1 is not considered prime)
Therefore m = 2357

The square numbers between 0 and 10 are  1, 4, 9 and in descending order 9,4.1so n = 941

m - n = 2357 - 941 = 1416

Unique prime factors of 1416 are 2,3,59

1416 as a product of prime factors = 2 × 2 × 2 × 3 × 59

Answer:

z = 30

Step-by-step explanation:

→ 360 ÷ z = 12

→ 360/z = 12

→ 12z = 360

→ z = 360/12

→ [ z = 30 ]

Hence, the value of z is 30.

Answer:you have to isolate z,make z the subject.

Step-by-step explanation: z=360 multiply by 12,

giving us 4320.z=4320,i mean thisis the answer you have to stick with if u want to find a value for z.

step by step;z/360=12

z=360 into 12

z=4320

Answer: P(A)=4/425≈0,0094.

Step-by-step explanation:

[tex]P(A)=\frac{C_4^1*C_3^1}{C_{51}^2} .[/tex]

The desk has 4 kings.

First card is drawn from a well shuffled deck is a card of king.     ⇒

[tex]C_4^1=\frac{4!}{(4-1)!*1!} =\frac{3!*4}{3!*1}=4.[/tex]

Second card is drawn from a well shuffled deck is a card of king too.    ⇒

[tex]C_{4-1}^1=C_3^1=\frac{3!}{(3-1)!*1!}=\frac{2!*3}{2!*1}=3.\\ The \ desk\ has\ 51\ card.\ \ \ \ \Rightarrow\\C_{51}^2=\frac{51!}{(51-2)*2!}=\frac{49!*50*51}{49!*1*2} =51*25=1275.\\ P(A)=\frac{4*3}{1275} =\frac{4}{425} \approx0,0094.[/tex]

The line b is perpendicular to the line y, then the line a will also perpendicular to the line y.  Then the correct option is B.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

If the line a is parallel to the line b, then the slope of the line a and b will be same.

The line b is perpendicular to the line y, then the line a will also perpendicular to the line y.

Then the correct option is B.

The diagram is given below.

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The equivalent expressions are 3(6x - 3) = 72 and 18x - 9 = 72

Given the equation below as shown;

3/5(30x - 15) = 72

Expand

3/5(30x) - 3/5(15) = 72

90x/5 - 15/5 = 72

3(6x - 3) = 72

Expand

18x - 9 = 72

Hence the equivalent expressions are 3(6x - 3) = 72 and 18x - 9 = 72

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By using trigonometric relations, we will see that:

x = √3

In the image, we can see a right triangle, where the hypotenuse measures √6, and the two legs have the same measure.

Then this is a 45°, 45°, 90° right triangle.

Then we can use the relation:

cos(a) = (adjacent cathetus)/(hypotenuse).

Where a = 45°, adjacent cathetus = x, hypotenuse = √6

Replacing that, we get:

cos(45°) = x/√6

Remember that cos(45°) = 1/√2

Replacing that we get:

1/√2= x/√6

√6/√2 = x

√(6/2) = x

√3 = x

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Answer:

mode: number that appears most

mode=4 and 7

mean: =3+4+5+6+7+8+9+10+11÷9=7

so mean is 7

Using a system of equations, it is found that £52 was originally shared.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

Angela and Michelle shared some money in the ratio 4: 9, hence, considering t as the total:

Angela gave Daniel half her share.Michelle gave Daniel a third of her share. Daniel was given a total of £20, hence:

[tex]\frac{x}{2} + \frac{y}{3} = 20[/tex]

[tex]\frac{4t}{26} + \frac{9t}{39} = 20[/tex]

[tex]\frac{12t + 18t}{78} = 20[/tex]

30t = 20 x 78

t = 20 x 78/30

t = £52.

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Step-by-step explanation:

if the area of each face of a cubical solid is 1764 CM square find its length

The rational number, 5/7 converted to a decimal is 0.714.

A rational number is a number that can be expressed as a fraction of two integers.

A decimal is a non-integer in which the integers are separated from the non integers by a point. In order to convert the fraction to a decimal, divide the numerator by the denominator.

5/7 = 0.714

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[tex]\displaystyle\lim_{t\to \infty}(20+100(0.3)^{0.2t})=20+100\lim_{t\to \infty}0.3^{0.2t}=20+100\cdot 0=20[/tex]

Answer:

x = 40

Step-by-step explanation:

All angles in a triangle add up to 180

(3x-10) + 30 + x = 180

4x = 160

x = 40

Answer: x = 40

Step-by-step explanation:

All the interior angles of a triangle add up to 180°

Therefore,

30 + 3x - 10 + x = 180

30 + 4x - 10 = 180

20 + 4x = 180

4x = 160

x = 40

The height of the pole is 96 feet

In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the legs a, b and the hypotenuse c, often called the Pythagorean equation:[1]

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

Create a diagram of the scenario first. You would have a right triangle with a hypotenuse (longest side) of h + 4, a longest leg of h - 68, and one leg of length h to represent the pole.

Set up the equation [tex]h^2 + (h - 68)^2 = (h + 4)^2[/tex] using the Pythagorean theorem ([tex]a^2 + b^2 = c^2[/tex]).

[tex]h^2 + (h - 68)^2 = (h + 4)^2[/tex]

On simplifying we get

[tex]h^2+h^2-136h+4624 = h^2+8h+16[/tex]

[tex]2h^2-136h+4624=h^2+8h+16[/tex]

[tex]h^2-144h+4608=0[/tex]

Solving using quadratic formula

[tex]h_{1,\:2}=\frac{-\left(-144\right)\pm \sqrt{\left(-144\right)^2-4\cdot \:1\cdot \:4608}}{2\cdot \:1}[/tex]  

[tex]h_1=\frac{-\left(-144\right)+48}{2\cdot \:1},\:h_2=\frac{-\left(-144\right)-48}{2\cdot \:1}[/tex]

h1 = 96 feet , h2 = 48 feet

If height would have been 48 feet then the other side would have a negative value as as 48 - 68 = -20 .

Hence the height of the pole is 96 feet

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Answer:

First, do 15/12 then take that and divide by 500!

Step-by-step explanation:

The rule for the reflection of the pre-image M(-5, 4), L(-4, 2), N(-2, 3), to form the image M'(-5, -4), L'(-4, -2), N'(-2, -3) is the option;

The given pre-image points are;

Possible third point; N(-2, 3)

The image points are;

The difference (change) between the pre-image and the image is a change in the sign of the y-value, which is equivalent to a reflection across the x-axis.

Therefore;

The rule for the reflection is therefore;

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Answer:

The answer might be C.(x=0)

The x intercept of the given line is (10, 0)

The x intercept of a line is the point where the line crosses the x-axis

It is the point where the value of y is zero

Given the equation of a line -2x+5y = -20

Substitute y = 0 into the equation

-2x +5(0) = -20

-2x = -20

x = 10

Hence the x intercept of the given line is (10, 0)

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Answer: 9 m

Step-by-step explanation:

[tex]75=\frac{1}{3}(25)(h)\\\\h=\frac{75}{25/3}=9[/tex]

Answer:

Hypotenuse = 8.94

Step-by-step explanation:

The value on the table above will be $30.6. Then the correct option is D.

The quantity of anything is stated as though it were a fraction of a hundred.

Raj was friends with his waitress, so he left her a 90 percent tip.

If his tip was $27.54.

Then the value in the table above will be

⇒ $27.54 / 0.90

⇒ $30.6

Then the correct option is D.

The complete question is given below.

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