David leaves reading at 11 45am. he arrives at cardiff at 1 45pm. david drives at an average speed of 56 miles per hour. work out the distance between bristol and cardiff

Step-by-step explanation:

your teacher was very nice and warned you about the trap in the question.

so, really, what do we have to do ?

a full circle represents 360°.

the shaded sector is the full circle minus the white sector !

this is the same as directly calculating the shaded sector for 360-75 = 285°.

so, the area of a circle is

pi×r²

in our case

pi×20² = 400pi

the needed fraction of the whole circle is either

75/360, if we want to subtract it for the solution

or

285/360, if we want to calculate the solution directly.

both lead to the same result.

400pi×360/360 - 400pi×75/360 =

= 400pi × 285/360 = 10pi × 285/9 = 2850pi/9 =

= 316.6666666...pi ≈ 316.7pi

Answer: 9

Step-by-step explanation:

78 subtract 51 is 27. One third of 27 is 9.

Answer:

pi is an irrational number, meaning that its decimal form neither ends (like 1/4 = 0.25) nor becomes repetitive

Step-by-step explanation:

In decimal form, the value of pi is approximately 3.14. But pi is an irrational number, meaning that its decimal form neither ends (like 1/4 = 0.25) nor becomes repetitive (like 1/6 = 0.166666...). (To only 18 decimal places, pi is 3.141592653589793238.)

The volume of a pyramid that fits exactly inside a cube is 9 cubic feet is 3 cubic feet

The formula for calculating the volume of a pyramid is expressed as:

V = Base area. * height/3

Since it is a cube with a volume of  9 cubic feet, the length of the cube will be:

l = ∛9
l = 2.08

Determine the volume of the pyramid

V = 9/3

V = 3 cubic feet

Hence the volume of a pyramid that fits exactly inside a cube is 9 cubic feet is 3 cubic feet

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Answer:

A

Step-by-step explanation:

The formula for a rectangular prism is length*width*height. Thus, the equation would be 6*4*16, which equals 384 cm^3.

Answer:

prism B is greater

Step-by-step explanation:

prism A

lenght: 1×4=4

width: 4×8=32

height: 8×1=8

add them all up and multiply it by 2 = 4+32+8×2=52

prism B

lenght: 10×2=20

width: 2×1.5=3

height:1.5×10=15

add them all up and multiply it by 2= 20+3+15×2=76

Answer:

[tex]22[/tex]

Step-by-step explanation:

Because:

[tex]a \times b = 2a - 3b + ab[/tex]

Then:

[tex]3 \times 5 + 5 \times 3[/tex]

[tex]6 - 15 + 15 + 10 - 9 + 15 \\ = 22[/tex]

Answer:

B. 22

Step-by-step explanation:

Given

3 x 5

5 x 3

⇒ 3 x 5 + 5 x 3

⇒ 6 + 16

⇒ 22 (Option B)

Answer:

∠ 1 = 36° , ∠ 2 = 144°

Step-by-step explanation:

∠ 1 and ∠ 2 are adjacent angles on a straight line and sum to 180° , that is

x + 12 + 6x = 180

7x + 12 = 180 ( subtract 12 from both sides )

7x = 168 ( divide both sides by 7 )

x = 24

Then

∠ 1 = x + 12 = 24 + 12 = 36°

∠ 2 = 6x = 6 × 24 = 144°

the standard equation of the circle having the given center and radius is [tex](x-9)^2+(y-2)^2=\frac{9}{25}[/tex].

Based on the exchange rate and Victor's budget, hector can see the sumo tournament and have about $322 left over.

Conversion rate of US dollars to Japanese yen = 1 : 94.153

Ratio of dollar to Yuan

1 : 94.153 = x : 5,488

1/94.153 = x / 5,488

1 × 5,488 = 94.153x

5,488 = 94.153x

x = 5,488 / 94.153

x = 58.2881055303601

Approximately,

x = $58

Amount left with Victor = Total money with Victor - amount spent

= $380 - $58

= $322

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Answer:

[tex]\large\begin{cases}a_1=5 \\a_n=a_{(n-1)}-4\end{cases}[/tex]

Step-by-step explanation:

Recursive formula allows us to find the value of a specific term based on the previous term.

Explicit formula allows us to find the value of a specific term based on its position.

Given explicit formula:  [tex]a(n)=5+(n-1)(-4)[/tex]

[tex]\implies a(1)=5+(1-1)(-4)=5[/tex]

[tex]\implies a(2)=5+(2-1)(-4)=1[/tex]

[tex]\implies a(3)=5+(3-1)(-4)=-3[/tex]

[tex]\implies a(4)=5+(4-1)(-4)=-7[/tex]

From inspection of the sequence, we can see that to get the next term, we need to subtract 4 from the previous term.

[tex]5 \underset{-4}{\longrightarrow} 1 \underset{-4}{\longrightarrow} -3 \underset{-4}{\longrightarrow} -7[/tex]

Therefore, the recursive formula is:

[tex]a_n=a_{(n-1)}-4[/tex]

For a recursive formula, we also need to give the value for [tex]a_1[/tex] .

Therefore, the final recursive formula for the explicit formula is:

[tex]\large\begin{cases}a_1=5 \\a_n=a_{(n-1)}-4\end{cases}[/tex]

Answer:

  D.  1/4

Step-by-step explanation:

You want to know the probability Marcy will miss a free throw, given that she makes 15 of 20.

We assume Marcy's record at practice is typical of her performance. It tells us that she makes 15/20 = 3/4 of the free throws she takes. That means she misses 1 -3/4 = 1/4 of the free throws.

The probability she will miss her free throw is 1/4.

__

Additional comment

Many assumptions are involved in this calculation. One of them is that her next throw is unaffected by her last throw. It is a rare player for whom that is the case.

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Answer:

50, 25

Step-by-step explanation:

The general pattern expressed by the sequence 800, 400, 200, 100 seems to be the previous number divided by 2. Therefore the next two numbers in this number pattern are most likely 100 / 2 = 50 and 50 / 2 = 25.

Answer:

50 and 25

Step-by-step explanation:

x / 2 is the constant

next number

100/2 = 50

next number

50/2 = 25

Answer:

7.2

Step-by-step explanation:

(6)^2 + (4)^2

36 + 16

52

square root of 52 = 7.2

Answer:

V = hpir^2 = 12(3.14)(3)^2 = 108(3.14) = 339.1

Step-by-step explanation:

Answer:

-38.

Step-by-step explanation:

Plug x = -3 into the given function

h(-3) = 2(-3)^3 + (-3)^2 + 7

= -54 + 9 + 7

= -54 + 16

= -38.

Answer: False

Step-by-step explanation:

I checked with a graphing app huhu... sorry TT

The vertices are (8, -1) , (-4, -1).

Parent function is general modulus function

Now

x is increased by +3 so change in x axis and vertex.

The vertex shifted 3 units leftwards .

Means compression factor is 2

Both graphs attached

Answer:

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis by a factor of}\:a[/tex]

Parent function:  [tex]f(x) = |x|[/tex]

Translated 3 units left:  [tex]f(x+3)=|x+3|[/tex]

Stretched parallel to the y-axis by a factor of 2:  [tex]2f(x+3)=2|x+3|[/tex]

Therefore, the function has been:

Attachments

Green graph - parent function   [tex]f(x) = |x|[/tex]

Red graph - Translated 3 units left   [tex]f(x)=|x+3|[/tex]

Blue graph - Stretched   [tex]f(x)=2|x+3|[/tex]

The lateral surface area is about 105,600 meters.

The area of ​​the pyramid is the measure relative to its surface and is obtained by the sum of the areas of the bases (polygonals) and of all the lateral faces (triangles). For the calculation of the lateral area of ​​a pyramid, we will have the perimeter of the base by the inclined height of the pyramid.

In this case, the formula of the lateral surface area is:

[tex]SA=\frac{P*S}{2}+B[/tex]

Where:

The height informed will not be used, it will only be a parameter to perform pythagoras, that is, we will find the hypotenuse of the triangle created by the height, like this:

[tex]S=\sqrt{(B)^2/2+H^2} \\S=\sqrt{110^2+70^2}\\S=\sqrt{17,000}\\ S=130[/tex]

Returning to the formula given above, we find that:

[tex]SA= \frac{(220*4)(130)}{2}+(220*220)\\ SA= 57,200+48,400= 105,600 \ meters[/tex]

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Answer:

(D. (-oo,0) U (0, oo )

[tex]( \infty 0)(0 \infty )[/tex]

(-oo,0) U (0, oo )

Answer:

the answer is 10z

Step-by-step explanation:

7+1=8

8+2=10

10z

Step-by-step explanation:

i just answered this.

the average change rate is the change of the functional result in a given interval relative (= divided by) to the length of the interval of the input variable.

in short

( f (interval upper limit) - f (interval lower limit) ) /

(interval upper limit) - (interval lower limit)

upper limit = 0

lower limit = -2

the functional values (y) are 6 and 10 at these points.

so, we get

(6 - 10) / (0 - -2) = -4 / 2 = -2

Using the Empirical Rule, it is found that she scores between 119 and 141 on 68% of the games that she bowls.

It states that, for a normally distributed random variable:

In this problem, considering that the mean is of 130 and the standard deviation is of 11, the interval between 119 and 141 is within one standard deviation of the mean, hence she scores between 119 and 141 on 68% of the games that she bowls.

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

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]

           What is the product of (x-3) and (x+7)?

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\diamond[/tex]

          First multiply the x's:-

x•x=x²

Now multiply x times 7:-

7x

So we have

x²+7x

Now multiply -3 times x:-

-3x

So we have

x²+7x-3x

Now multiply 7 and -3:-

x²+7x-3x-21

On simplification,

x²+4x-21

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

The written form of the expression of (4 × 10 ) + ( 3 × 1/100)+(5×1/1000) is given as 4.035.

A standard form of a number is known to be the used in writing the number in a way that follows a specific rules.

Therefore, The written form of the expression of (4 × 10 ) + ( 3 × 1/100)+(5×1/1000) is given as 4.035.

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Answer:

2 to the power of three × 3 × 5

Step-by-step explanation: