A bookshop has a sale.
A book normally costing $39.95 is priced at $23.97.
By what percentage has the price been reduced?

please show working out

The probability is 1:2

Answer:

4/18

Step-by-step explanation:

You have 5 WHITE marbles and 5 Black marbles.

The probability of drawing a WHITE marble is 5/10  or 1/2

And the probability of drawing the second (marble another WHITE marble) is 4/9

So 1/2 x 4/9 = 4/18 or 5/10 x 4/9 = 20/90 / 5 = 4/18

Therefore the probability of drawing a WHITE marble not replacing it then drawing another WHITE marble is 4/18

Answer:

Option D 4 inches is correct.

Step-by-step explanation:

Area of trapezoid = 48 square inches

Base a = 9

Base b = 15

We need to find the height h.

The formula for area of trapezoid is

Area = (a+b)/2 * h

Putting the values, we get

48 = ( 9+15)/2 * h

48 = (24)/2 * h

48 = 12 *h

=> h = 48/12

h = 4 inches

So, Option D 4 inches is correct.

Answer:

4 in.

Step-by-step explanation:

The area of a trapezium is calculated using the formula:

[tex]Area=\frac{1}{2}(Sum\:of\:the\:bases)\times height[/tex]

The given tra-pezoid has area [tex]48[/tex] square inches.

The bases are given as 9 inches and 15 inches.

We plug in the known values into the formula to get;

[tex]48=\frac{1}{2}(9+15)\times height[/tex]

[tex]48=\frac{1}{2}(24)\times height[/tex]

[tex]48=12\times height[/tex]

Divide both sides by 12.

[tex]\frac{48}{12}=height[/tex]

[tex]4 in.=height[/tex]

Therefore the height of the trapezoid is 2 inches.

I did this earlier for a senior but believed I got it wrong based on that I fixed it to this : 62.5 was the percentage so 6250% so 18x 62.5 1125 HEY that’s reasonable please keep in mind I’m in middle school and you should double check this

From conservation of angular velocity the larger pulley will rotate at a speed of 500 rpm.

The conservation of angular velocity states that the angular velocity for a conjugate system will be always equal to the angular velocity of a part of the same system.

Mathematically -

r1ω1 = r2ω2 = r3ω3 = ................. = rnωn

where r is the radius of the circular belts, ω is the angular velocity and n is the total number of segments in the conjugate system.

Given that a pair of belted pulleys have diameters of 18 in. and 12 in. Also given that the smaller pulley turns at 750 rpm.

The radius of the pulleys are 9 in. and 6 in. respectively.

Let x rpm be the speed of the larger pulley turn.

From conservation of angular velocity, we have

⇒ 6 * 750 = 9 * x

⇒ x = (6 * 750)/9

∴  x = 500 rpm

Therefore, from conservation of angular velocity the larger pulley will rotate at a speed of 500 rpm.

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Final answer:

The expressions 2(x+3) and 2x+4+2x are not equivalent.

Explanation:

To determine if the expressions 2(x+3) and 2x+4+2x are equivalent, we can simplify them and compare the results. Let's simplify each expression when x=1:

2(x+3) = 2(1+3) = 2(4) = 8

2x+4+2x = 2(1)+4+2(1) = 2+4+2 = 8

Both expressions evaluate to 8 when x=1, so they are equivalent. Now, let's evaluate the first expression when x=2:

2(x+3) = 2(2+3) = 2(5) = 10

The first expression evaluates to 10 when x=2, which is different from the value of 8 obtained from the second expression. Therefore, the expressions 2(x+3) and 2x+4+2x are not equivalent.

Answer:

The surface area of the composite figure is [tex]285.7\ units^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the composite figure is equal to the lateral area of the rectangular prism plus the area of the base of rectangular prism plus the lateral area of the pyramid

[tex]SA=2(5+6)(7)+(5)(6)+2[\frac{1}{2}(6)(9.2)] +2[\frac{1}{2}(5)(9.3)]\\ \\SA=154+30+55.2+46.5\\ \\SA=285.7\ units^{2}[/tex]

Karla in her work does not consider the area of the base of the rectangular prism.

Answer:

B-She left out one of faces of the solid. She should have simplified

Step-by-step explanation:

the dude before me is wrong i got 100%

help a brother out find me on ticktock and gramy - yrkjncl

ANSWER

[tex] \sum _{n = 1} ^{6} 2n[/tex]

EXPLANATION

The series is:

2 + 4 + 6 + 8 + 10 + 12

The first term is:

f(1)=2

The common difference is

[tex]d= 4 - 2 = 2[/tex]

The formula for the corresponding sequence is

[tex]f(n) = 2 + 2(n - 1)[/tex]

[tex]f(n) = 2 + 2n - 2[/tex]

[tex]f(n) = 2n[/tex]

The summation notation is:

[tex] \sum _{n = 1} ^{6} 2n[/tex]

Answer:

2.5 m

Step-by-step explanation:

Consider the ramp, the ground and the back of the lorry to form a right triangle where the ramp is the hypotenuse and the distance from the back of the lorry is the adjacent side, x

Using the cosine ratio in the right triangle

cos32° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{3}[/tex]

Multiply both sides by 3

3 × cos32° = x, hence

x ≈2.5 m

Answer:

Pemdas subtracting would be last

Step-by-step explanation:

The operation should perform last to evaluate the expression is Addition.

The order of operations, or BODMAS, is a method for carrying out operations in an arithmetic statement.

B - Brackets, O - Order of powers or roots, (in some cases, 'of'), D - Division, M - Multiplication A - Addition, and S - Subtraction.

We have the expression,

(7×4)+(10÷2)×(14.7−9)

Now, using BODMAS first division is performed.

(7×4)+ 5 x (14.7−9)

Now, Multiplication is performed

28 + 5 x (14.7-9)

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The probability that the sum of the two resulting numbers is greater than 5 is 2/3

The probability that the product of the two resulting numbers is odd is 1/3

How to determine the required probabilities

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

Die = {1, 2, 2, 4}

Spinner = {3, 4, 7}

The sample space is represented as

Space = {(1, 3), (1, 4), (1, 7), (2, 3), (2, 4), (2, 7), (2, 3), (2, 4), (2, 7), (4, 3), (4, 4), (4, 7)}

For the sum greater than 5, we have the following space

Space = {4, 5, 8, 5, 6, 9, 5, 6, 9, 7, 8, 11}

In the above, we have

Total = 12

Sum greater than 5 = 8

So, this probability is

P = 8/12 = 2/3

For the product resulting in odd numbers, we have the following space

Space = {3, 4, 7, 6, 8, 14, 6, 8, 14, 9, 12, 21}

In the above, we have

Total = 12

Odd results = 4

So, this probability is

P = 4/12 = 1/3

Hence, the probabilities are 2/3 and 1/3

The two tangent lines for each circle are the same length. Set the equations to equal and solve for x.

1. 4x + 3 = 3x +12

Subtract 3x from each side:

x +3 = 12

Subtract 3 from both sides:

x = 9

2. -2 + x = 2x -7

Subtract 2x from both sides:

-2 - x =  -7

Add 2 to each side:

-x = -5

Multiply both sides by -1:

x = 5

The value of x for both the circles is 9  and 5 .

A tangent for a circle is defined as a straight line which touches the circle at just one point.

The tangent is perpendicular to the radius of the circle at the point of where tangent touches the circle.

It is given in the question to find the value of x

When two tangents meet at a point C , the distance between the point of tangency and the point C is equal for both the tangent.

Therefore for the given circle

For first circle to solve for x , we will equate the two distances

4x + 3 = 3x +12

x +3 = 12

x = 9

-2 + x = 2x -7

-2 - x =  -7

-x = -5

x = 5

Therefore the value of x for both the circles is 9  and 5 .

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Answer:

Part 1) [tex]20\ students[/tex]

Part 2) [tex]95\%[/tex]

Part 3) [tex]9\ games[/tex]

Step-by-step explanation:

Part 1) Using proportion

[tex]\frac{15}{75\%}=\frac{x}{100\%}\\ \\x=15*100/75\\ \\x=20\ students[/tex]

Part 2) Using proportion

[tex]\frac{40}{100\%}=\frac38}{x\%}\\ \\x=100*38/40\\ \\x=95\%[/tex]

Part 3) Using proportion

[tex]\frac{18}{100\%}=\frac{x}{50\%}\\ \\x=18*50/100\\ \\x=9\ games[/tex]

Answer:

what he said

Step-by-step explanation:

The answer is D. because when you solve the equation by combining expressions and isolating the variable, both equations have 2 solutions-

Answer:

D

Step-by-step explanation:

Answer:

2x+7

Step-by-step explanation:

Answer:

Graph of given function doesn't exist.

Step-by-step explanation:

Given equation is [tex]|x|=-2[/tex].

Now we need to determine about how do you graph [tex]|x|=-2[/tex].

We know that [tex]|x|[/tex] represents absolute value function.

By definition of absolute value function, we know  that output of [tex]|x|[/tex] must always be positive.

But in given equation [tex]|x|=-2[/tex], we have output -2 which is negative.

That is not possible.

Hence there is no solution to the given problem [tex]|x|=-2[/tex].

So the graph of given function doesn't exist.

Answer:

25 + 144 = 169

Step-by-step explanation:

Take a look at the first possible answer:

5² + 12² = 13².  Is this true or not?

25 + 144 = 169, which is equal to 13².   This set of side lengths represents a right triangle.

Answer:

5² + 12² = 13²

Step-by-step explanation:

[tex] {5}^{2} + {12}^{2} = 25 + 144 = 169 \\ \\ \sqrt{169} = ±13[/tex]

I am joyous to assist you anytime.

13/8

fraction

I think cause you nees to add all of the socks together and put how many socks was black

Hello there!

Answer:

8/13

Step-by-step explanation:

In order to find the probability in questions like this, we would need to find the number that we want to get and the total amount of possibilities.

Important information in the text:

With the information, we can find the probability.

In the question, we are trying to find the probability of picking out a black sock, and there is 8 black socks. The 8 will go on our numerator.

Our denominator would be the total amount of things that leads to our probability. Since we only have 8 black socks and 5 yellow socks, we would add 8 + 5 to get the total amount of socks.

8 + 5 = 13

The 13 will go in the denominator.

When you put all of the stuff together, you should get 8/13. You can't simplify it because 13 is an odd number that can't get any smaller.

8/13 is the probability of picking out a black sock

These lines are only parallel lines because these lines don't touch each other and parallel lines don't touch each other.

Answer:

These lines are only parallel.

Answer:

A

Step-by-step explanation:

means that as the value of one variable increases, the value of the other variable increases; as one decreases the other decreases.

Answer:

x=9   x=-1

Step-by-step explanation:

We can factor

x^2 -8x-9 =0

What 2 numbers multiply to -9 and add to -8

-9*1 = -9

-9 +1 = -8

(x-9) (x+1) =0

Using the zero product property

x-9 =0   x+1 =0

x=9   x=-1

Answer:

75 in^3

Step-by-step explanation:

i know because i had the test, and the other persons answer is wrong :)

Answer:

27 meters

Step-by-step explanation:

a=1/2bh

a=1/2(18)(6)

a=27

Multiply the two numbers.

48*60=2880 inches

I think this is the way to answer this question.

Answer:

[tex]\large\boxed{x<4\to x\in(-\infty,\ 4)}[/tex]

Step-by-step explanation:

[tex]-4x+28>12\qquad\text{subtract 28 from both sides}\\\\-4x>-16\qquad\text{change the signs}\\\\4x<16\qquad\text{divide both sides by 4}}\\\\x<4[/tex]

Answer: Rob ate more crackers.

Symbol answer: 6/12 < 9/12

Step-by-Step explanation:

Common knowledge: Anytime you have the same numerator, with a different denominator, the one with the bigger denominator is always smaller. For example, if had a pizza with 6 slices and a pizza with 4 slices, the one with 6 slices and smaller and the one with 4 slices and bigger. Even though 6>4 that mindset has to change when thinking about a problem like this.

Another explanation:

If you still don’t get it, simply find a common denominator, so we’ll choose 12. Take 3/6 and multiply that by 2/2 so you get 6/12 and then take 3/4 and multiply that by 3/3 on both the (numerator and denominator) and that equals 9/12.

So now you have the expression: 6/12<9/12.

Check the picture below.

Answer:

B

Step-by-step explanation:

B is the correct answer.  Since Mrs. Hooper and Mr. Anderson had to call a total of 8 parents, you know the first equation must be either A or B (H + A = 8).

Since you know that Mrs. Hooper had to call 2 more parents than Mr. Anderson, the equation will have to have H + 2 on one side; that's how you know the correct answer is B.

The set of equations which correctly describes the phone calls made is A. H + A = 8 ; H = A + 2.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

H denote the number of calls Mrs. Hooper made and A denote the number of calls Mr. Anderson made.

Mrs. Hooper and Mr. Anderson had to call a total of eight parents.

So, the equation representing this is, H + A = 8

Mrs. Hooper needed to call two more students than Mr. Anderson.

H = A + 2

So the set of equations are,

H + A = 8 ; H = A + 2

Hence the correct option is A. H + A = 8 ; H = A + 2

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Answer:

[tex]y=4\sin(\frac{3}{2}x+\frac{2\pi}{3})[/tex]

Step-by-step explanation:

The graph of the cosine function can be obtained by shifting the sine function to the left by [tex]\frac{\pi}{2}[/tex] units.

The given cosine function is:

[tex]y=4\cos(\frac{3}{2}x+\frac{\pi}{6})[/tex]

When we shift this function to the left by [tex]\frac{\pi}{2}[/tex] units, we obtain a sine function

[tex]y=4\sin(\frac{3}{2}x+\frac{\pi}{6}+\frac{\pi}{2})[/tex]

[tex]y=4\sin(\frac{3}{2}x+\frac{2\pi}{3})[/tex]

These two functions have the same graph

The second option is correct.

Answer:

D) The number of bacteria decreases by 7% each hour.

Step-by-step explanation:

Exponential functions describe situations where values do not increase at a linear or constant rate. Adding or subtracting every year or hour will result in a linear function, so A, B, and C are incorrect.

Option (D) The number of bacteria decreases by 7% each hour is correct.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]

where 'a' is a constant and a>1

As we know, the exponential function increases rapidly according to the exponent.

It is not a linear function, and it never gives a negative value if the value of a>0

As the no other information was given.

Thus, option (D) The number of bacteria decreases by 7% each hour is correct.

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Answer:

The graph in the attached figure

Step-by-step explanation:

we have

y-x> 0 -----> inequality A

y> x

The solution of the inequality A is the shaded area above the dashed line y=x

x+1<0 ----> inequality B

x < -1

The solution of the inequality B is the shaded area at the left of the dashed line x=-1 (open circle)

therefore

The solution of the system of inequalities in the attached figure

Answer: x<5

How?

-3x-12>3

(Add 12 to both sides)

-3x>15

(Divide -3 by 15)

x<5

(Remeber to flip the signs since you are dividing by a negative.)