solve the equation 4(-x+4)=12

There are 24 permutations of the letters a, b, c, d taken four at a time, calculated using the formula 4!.

The question revolves around finding the number of permutations of the letters a, b, c, d taken four at a time. To solve this, we need to understand that a permutation represents the arrangement of all members of a set in every possible order.

In the case of the letters a, b, c, d, we want to arrange them in all possible ways where order matters and taking all four at a time. The formula to calculate permutations is P(n, r) = n! / (n-r)!, where n is the total number of items to choose from, and r is the number of items to choose. However, since we are taking all four letters each time, we are essentially looking for 4!, which simplifies to 4*3*2*1.

Therefore, 4! equates to 24. This means there are 24 possible ways to arrange the letters a, b, c, d when taking all four at a time. It's an excellent exercise to manually write out all of these permutations to get practical experience with the concept.

The solution is: The retail price is $6.50.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

Here, we have,

given that,

The total price of an article is $7.02, including tax.

If the tax rate is 8%

Lets price of article = x

Tax  is 8%  of article = 0.08x

so, we get,

x+0.08x=7.02

1.08x=7.02

x=7.02/1.08

x=6.5

The retail price is $6.50.

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The probability that her keys have landed within the forest will be C. 0.8.

From the information given, the blacked out middle section of the pyramid is 20 acres. Therefore, the probability will be:

= 20/100 = 0.2

Now, the probability that her keys have landed within the forest will be:

= 1 - 0.2

= 0.8

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We know that co terminal angles are those angles which have a difference equal to a multiple of 360 degrees. For example co terminal angle of 45 degrees is 76 degrees because their difference is equal to 720 degrees, which is a multiple of 360.

We have been given an angle 425 degrees.

From the given choices, we need to check if angles being added or subtracted to 425 degrees are multiples of 360 or not.

Let us check each of the options one by one.

(A) The angle being subtracted is [tex]1000n[/tex]. Therefore, we have [tex]\frac{1000n}{360}=2.77n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.

(B)

The angle being subtracted is [tex]840n[/tex]. Therefore, we have [tex]\frac{840n}{360}=2.33n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.

(C)

The angle being added is [tex]960n[/tex]. Therefore, we have [tex]\frac{960n}{360}=2.67n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.

(D)

The angle being added is [tex]1440n[/tex]. Therefore, we have [tex]\frac{1440n}{360}=4n[/tex], which is an integer for all values of n. Therefore, angle given in this option is indeed a co terminate angle to 425 degrees.

Hence, correct answer is option (D).

Answer:

LCM (8,10) = 2 × 2 × 2 × 5 = 40

Step-by-step explanation:

Least common multiple is the smallest number that is multiple of both the given numbers.

Example: LCM of 2 and 3 is 6 .

6 is a multiple of both 2 and 3 .

Given numbers are 8 and 10

First write both in factor form,

⇒ 8 = 2 × 2 × 2

⇒ 10 = 2 × 5

We find LCM by writing common terms one times and multiplying all terms together,

Here, 2 is common to both 8 and 10 so we write it once only.

Thus, LCM (8,10) = 2 × 2 × 2 × 5 = 40.

The volume of figure is 877.876 yd³

1. Volume of Cone

= 1/3πr²h

= 1/3 x 3.14 x 2 x 2 x 4

= 16.746

2. Volume of cylinder

= 3.14 x 2 x 2 x 8

= 100.48

3. Volume of Hemisphere

= 2/3πr³

= 7.065

4. Volume of cylinder

= 3.14 x 1.5 x 1.5 x 9

= 63.585

5. Volume of prism

= 1/2 x ( 6 x 6) x 12

= 216

6. Volume of Cuboidal prism

= l w h

= 6 x 6 x 12

= 432

7. Volume of pyramid

= 1/3 x 3 x 2

= 2

8. Volume of cuboidal prism

= 10 x 2 x 2

= 40

So, the volume of figure is

= 16.746 + 100.48 + 7.065 + 63.585 + 216 + 432 + 2 + 40

= 877.876 yd³

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In the parallelogram CDKM the value of the line segment CD and DK is 10 units and 17 units.

Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.

The quadrilateral CDKM is a parallelogram. In this parallelogram, the side DA is perpendicular to the side CK.

The difference of the side DK and CD is,

[tex]DK - CD = 7\\DK=7+CD[/tex]

The length of the line segment CA and AK is 6 units and 15 units respectively.Then by the Pythagoras theorem,

[tex](AD)^2=(CD)^2-(AC)^2\\(AD)^2=(CD)^2-(6)^2[/tex]              ....1

Again by using the Pythagoras theorem

[tex](AD)^2=(Dk)^2-(AK)^2\\(AD)^2=(DK)^2-(15)^2[/tex]

Put the value of (AD)², from equation 1 in the above equation as,

[tex](CD)^2-6^2=(DK)^2-(15)^2\\(CD)^2-36=(DK)^2-225[/tex]

Put the value of DK in the above equation as,

[tex](CD)^2-36=(7+CD)^2-225\\(7+CD)^2-(CD)^2=225-36\\(CD)^2+14CD+49-(CD)^2=189\\CD=10[/tex]

Hence, the value of DK is,

[tex]DK=7+10DK=17[/tex]

Hence, In the parallelogram CDKM the value of the line segment CD and DK is 10 units and 17 units.

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Answer:

Option A is correct that is x° = 56°

Step-by-step explanation:

Let Given Lines are tangents.

So we use a result which states that Tangents are perpendicular with radius at point of contacts.

⇒ ∠ B = ∠ D = 90°

Angle sum property of Quadrilateral = 360°

⇒ ∠A + ∠B + ∠O + ∠D = 360

x + 90 + 124 + 90 = 360

x + 304 = 360

x = 360 - 304

x = 56

Therefore, Option A is correct that is x° = 56°

Answer:

y = 75 - 3x

Step-by-step explanation:

Let the number of token left = y

total number of token bought = 75

Number of games played by Conor = x

It is given for playing one game, the price = 3 token

Therefore for playing x games, the price is = 3x

Therefore, the number of tokens left with Conor is given by

  y = 75 - 3x

Thus, the expression that is equivalent to the number of remaining tokens is

y = 75 - 3x

The ball's maximum height is [tex]\( \boxed{22} \)[/tex] feet.

To find the time at which the ball reaches its maximum height, we can first determine the vertex of the quadratic function [tex]\( h(t) = -16t^2 + 32t + 6 \),[/tex] where t represents time in seconds and h represents height in feet.

The vertex of a quadratic function [tex]\( ax^2 + bx + c \)[/tex] is given by the formula:

[tex]\[ t_{\text{max}} = \frac{-b}{2a} \][/tex]

For the function [tex]\( h(t) = -16t^2 + 32t + 6 \)[/tex], we have a = -16 and b = 32 . Plugging these values into the formula:

[tex]\[ t_{\text{max}} = \frac{-32}{2(-16)} \]\[ t_{\text{max}} = \frac{-32}{-32} = 1 \][/tex]

So, the ball reaches its maximum height at t = 1  second.

To find the maximum height, we substitute t = 1 into the function h(t) :

[tex]\[ h(1) = -16(1)^2 + 32(1) + 6 \]\[ h(1) = -16 + 32 + 6 \]\[ h(1) = 22 \][/tex]

Therefore, the ball's maximum height is [tex]\( \boxed{22} \)[/tex] feet.

Answer:

D. 12 on edge

Step-by-step explanation:

I think the answer is Probability is (1513+99)/(1414+99+1111+99)=1612/2723

Answer:

33

Step-by-step explanation: