evaluate
the expression when
C = 6 and Y = -7
7-у

The numbered spot at which all the runners will be next to one another is spot 19.

Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.

Starting with the runner on the outside track, the provided parameters are;

The runner covered n₁ = 5 places on the outside track, which is the number of spaces.

Next, the inner runner will traverse n₂ spaces, which equals one space.

The following inner runner will cover n₃ = 3 spaces.

The subsequent runner will traverse n₄ = 2 spaces.

The Lowest Common Multiple, or LCM, of all the runners' speeds or the total number of spaces they cover in the same amount of time, determines where all the runners will be placed next to one another.

LCM(5, 1, 3, 2) = 30 is the LCM of 5, 1, 3, and 2.

Time = 30/ = 6

Consequently, when the first runner has covered 30 places, we have;

Six time units have been expended.

The runner comes to a stop at position 30- (30 -19) = Position 19.

First runner's new destination is Spot 19.

The distance covered simultaneously by runner 2 is 6 x 1 = 6.

The distance covered by two runners running simultaneously equals six spaces.

Second runner's new position: 6 spaces plus spot 13 equals spot 19.

The combined distance covered by the three runners is 6 x 3 = 18.

The distance runner 3 covers 18 spaces simultaneously.

Third runner's new position: 18 spaces + Spot 1 = 19 spaces

Runner 4 covers a distance of 6 x 2 = 12 at the same time.

Distance runner 4 journeys equals 12 spaces

Runner 4's new position is now 12 spaces Plus Spot 7 = Spot 19.

Therefore, all the runners will be next to one another is spot 19.

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Answer:

23182 or 23181.5109105

Step-by-step explanation:

Step 1: Write the dividend and divisor:

\(\sf\:\frac{{x^3 - 8x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 2: Divide the first term of the dividend by the first term of the divisor:

\(\sf\:\frac{{x^3}}{{x}} = x^2 \\ \)

Step 3: Multiply the divisor (x - 4) by the result (x^2):

\(\sf\:(x - 4) \cdot (x^2) = x^3 - 4x^2 \\ \)

Step 4: Subtract the result from the original dividend:

\(\sf\:(x^3 - 8x^2 + 6x + 41) - (x^3 - 4x^2) = -4x^2 + 6x + 41 \\ \)

Step 5: Bring down the next term from the dividend:

\(\sf\:\frac{{-4x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 6: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-4x^2}}{{x}} = -4x \\ \)

\(\sf\:(x - 4) \cdot (-4x) = -4x^2 + 16x \\ \)

\(\sf\:(-4x^2 + 6x + 41) - (-4x^2 + 16x) = -10x + 41 \\ \)

Step 7: Bring down the next term from the dividend:

\(\sf\:\frac{{-10x + 41}}{{x - 4}} \\ \)

Step 8: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-10x}}{{x}} = -10 \\ \)

\(\sf\:(x - 4) \cdot (-10) = -10x + 40 \\ \)

\(\sf\:(-10x + 41) - (-10x + 40) = 1 \\ \)

Step 9: There are no more terms to bring down, so the division is complete.

Step 10: Write the final result:

The quotient is \(\sf\:x^2 - 4x - 10\\\) and the remainder is 1.

Therefore, the division of \(\sf\:(x^3 - 8x^2 + 6x + 41) by (x - 4) \\\) is:

\(\sf\:(x^3 - 8x^2 + 6x + 41) ÷ (x - 4) \\ \) \(\sf\:= x^2 - 4x - 10 + \frac{{1}}{{x - 4}} \\ \)

Loudness, pitch, and timbre are the three psychological aspects of sound that are influenced by the physical properties of sound waves.

When energy moves through a medium (such as air, water, or any other liquid or solid matter), it creates a pattern of disturbance known as a sound wave that propagates away from the sound source.

When an object vibrates, sound waves are produced that are similar to pressure waves, like when a phone rings.

Pitch, intensity, and timbre are three key components of the field of sound psychology or psychoacoustics. People can distinguish the harmonics of a complex periodic sound wave under certain conditions thanks to the way that humans perceive sound and music.

Thus, loudness, pitch, and timbre are the three psychological aspects of sound that are influenced by the physical properties of sound waves.

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Answer:

x = -1 and y = 1

Step-by-step explanation:

5x + 2y = -3 . . . . . . . (i)

x + 5y = 4 . . . . . . . (ii)

x + 5y = 4

x = 4 - 5y

5(4 - 5y) + 2y = -3

20 - 25y + 2y = -3

-23y = - 23

y = 1

5x + 2(1) = -3

5x + 2 = -3

5x = - 5

x = -1

Answer:

$15.00 per day and $0.22 per mile.

Step-by-step explanation:

To determine the daily fee and mileage fee charged by Best Rentals, we can set up a system of equations based on the given information.

Let's assume the daily fee is represented by "d" and the mileage fee is represented by "m."

For Mateo:

3d + 300m = 111.00

For Dara:

5d + 600m = 207.00

Now we can solve this system of equations to find the values of "d" and "m."

Multiplying the first equation by 2 to eliminate "m," we get:

6d + 600m = 222.00

Subtracting the second equation from this equation, we have:

(6d + 600m) - (5d + 600m) = 222.00 - 207.00

d = 15.00

Substituting the value of "d" into the first equation, we can solve for "m":

3(15.00) + 300m = 111.00

45.00 + 300m = 111.00

300m = 111.00 - 45.00

300m = 66.00

m = 0.22

Therefore, Best Rentals charges $15.00 per day and $0.22 per mile.

Answer:

The confidence interval is  \(25.16 < \mu < 26.85\)

Step-by-step explanation:

From  the question we are given a data set

     25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7.

The mean of the this sample data is  

       \(\= x = \frac{\sum x_i}{n}\)

where is the sample size with values  n =  10

         \(\= x = \frac{25.5+ 26.1+ 26.8+23.2+ 24.2+ 28.4+ 25.0+ 27.8+ 27.3+ 25.7}{10}\)

          \(\= x = 26\)

The standard deviation is evaluated as

             \(\sigma = \sqrt{\frac{\sum (x-\= x)}{n} }\)

substituting values

     \(= \sqrt{\frac{ ( 25.5-26)^2, (26.1-26)^2, (26.8-26)^2, (23.2-26)^2}{10} }\)

                  \(\cdot \ \cdot \ \cdot \sqrt{\frac{ ( 24.2-26)^2, (28.4-26)^2+( 25.0-26)^2+ (27.8-26)^2+( 27.3-26)^2+( 25.7-26)^2}{10} }\)

     \(\sigma = 1.625\)

The  confidence level is given as 90% hence the level of significance is calculated as

    \(\alpha = 100 -90\)

    \(\alpha =10\)%

   \(\alpha = 0.10\)

Now the critical values of \(\frac{\alpha }{2}\) is obtained from the normal distribution table as

      \(Z_{\frac{\alpha }{2} } = 1.645\)

The reason  we are obtaining  the critical values of \(\frac{\alpha }{2}\) instead of  \(\alpha\) is because  we are considering two tails of the area under the normal curve

  The margin of error is evaluated as

            \(MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }\)

substituting values

           \(MOE = 1.645 * \frac{1.625 }{\sqrt{10} }\)

           \(MOE = 0.845\)

The  90%, two sided confidence interval is mathematically evaluated as

           \(\= x - MOE < \mu < \= x + MOE\)

           \(26 - 0.845 < \mu < 26 + 0.845\)

           \(25.16 < \mu < 26.85\)

Given that the lower and the upper limit is greater than  25 then we can assure the manufactures  that the battery life exceeds 25 hours

Step-by-step explanation:

(-8-9)+23

-17+23

6.........

The value of algebraic expression [(-8) + ( -9)] + 23 is 6.

Here,

We have to simplify;  the sum of -8 and -9, increased by 23.

And, find an algebraic expression.

What is Algebraic expression?

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations.

Now,

The written expression is, the sum of -8 and -9, increased by 23.

It can be written as,

⇒ [(-8) + ( -9)] + 23

⇒ - 8 - 9 + 23

⇒ - 17 + 23

⇒ 6

Hence, The value of algebraic expression [(-8) + ( -9)] + 23 is 6.

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Answer:

25

Step-by-step explanation:

Answer:

25

Step by step explanation:

Hey

Answer:

144in square

Step-by-step explanation:

Answer:

1282kg

Step-by-step explanation:

1.0*1.12*1.1=1.232 tonnes

50kg + 1232kg = 1282kg

Hope this helps :)

Answer:

88

Step-by-step explanation:

Answer:

A, B, E

Step-by-step explanation:

Notice that A, B, and E all maintain their common ratios, while C and D do not.

Answer:

The sample mean (x⁻ ) is the point of estimate of the Population mean

x⁻ = 7.7

The sample standard deviation   (S)  is the point of estimate of the Population standard deviation

 S = 3.65

Step-by-step explanation:

Step(i):-

Given data    12  7  6  3   5   12   9   10  11  2

Mean of the data

          \(x^{-} = \frac{12+7+6+3+5+12+9+10+11+2}{10} = 7.7\)

x          :     12      7       6       3        5         12      9       10           11        2

x-x⁻      :   4.3     -0.7    -1.7   -4.7    -2.7     4.3    1.3      2.3         3.3     -5.7

(x-x⁻  )² :  18.49  0.49   2.89  22.09 7.29  18.49 1.69    5.29  10.89   32.49

Step(ii):-

Standard deviation of the sample

\(S^{2} = \frac{sum (x-x^{-})^{2} }{n-1} = \frac{120.1}{10-1} = 13.344\)

Standard deviation of the sample

 S = √13.344 =3.65

Final answer:-

The sample mean (x⁻ ) is the point of estimate of the Population mean

x⁻ = 7.7

The sample standard deviation   (S)  is the point of estimate of the Population standard deviation

 S = 3.65

The values of the addition given will be:

6 + 9 = 15

0 + 9 = 9

2 + 3 = 5

11 + 90876 = 90887

Addition simply means sum. It is one of the basic operations that are used in Mathematics. In this case, the addition of two whole numbers will bring about the total amount of the value combined.

Therefore the addition will be the sum of the numbers. This will be:

6 + 9 will be:

= 6 + 9

= 15

0+9 will be:

= 0 + 9

= 15

2+3 will be:

= 2 + 3

= 5

11+90876 will be:

= 11 + 90876

= 90887

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Answer:

a

\(A_w  =  1.667  \ hour \)

b

 \(b  =  0.667 \  hour  \)

Step-by-step explanation:

From the question we are told that

   The mean number of ticket per hour is  \(\mu  =  12 \  tickets\)

   The  mean number of customers arrive to purchase tickets each hour is \(\lambda  =  8 \  customers\)

    Generally the average time the ticket buyer must wait is mathematically represented as

      \(A_w  =  \frac{\lambda }{ \mu [\mu -\lambda]}\)

=>    \(A_w  =  \frac{8 }{ 12 [12-8]}\)

=>     \(A_w  =  1.667  \ hour \)

Generally the portion of time is the ticket seller busy is mathematically represented as

     \(b  =  \frac{\lambda}{ \mu}\)

=>    \(b  =  \frac{8}{ 12} \)

=>    \(b  =  0.667 \  hour  \)

The decimal representation of 1/70000000 is 0.0000000142857142857....

In math, what is a fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

To find the digit that occurs in the 2023rd place after the decimal point, we can use long division to divide 1 by 70000000 and track the remainders.

Since the decimal representation of 1/70000000 is repeating every 6 digits, we can find the digit at the 2023rd place by taking the remainder when 2023 is divided by 6.

2023 % 6 = 1

So the digit in the 2023 place is the first digit after the repeating decimal, which is 4.

Therefore the digit in the 2023rd place after the decimal point is 4.

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Given:

Vertices of a square are A(-4,6), B(5,6) C(4,-2), and D(-5,-2).

To find:

The intersection of the diagonals of square ABCD.

Solution:

We know that diagonals of a square always bisect each other. It means intersection of the diagonals of square is the midpoint of diagonals.

In the square ABCD, AC and BD are two diagonals. So, intersection of the diagonals is the midpoint of both AC and BD.

We can find midpoint of either AC or BD because both will result the same.

Midpoint of A(-4,6) and C(4,-2) is

\(Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)

\(Midpoint=\left(\dfrac{-4+4}{2},\dfrac{6+(-2)}{2}\right)\)

\(Midpoint=\left(\dfrac{0}{2},\dfrac{6-2}{2}\right)\)

\(Midpoint=\left(\dfrac{0}{2},\dfrac{4}{2}\right)\)

\(Midpoint=\left(0,2\right)\)

Therefore, the intersection of the diagonals of square ABCD is (0,2).

The area of ​​the triangular pyramid is 787.27 mm²

The volume of a right-angled triangular pyramid  is given by the formula V = 1 3 × B × h, where B is the area of ​​the base of the triangle and h is the height (the distance from the apex to the base).

 To calculate the  area of ​​a triangular pyramid, we need to find the area and base of the four triangles.

First, we find the area of ​​the base of an equilateral triangle. The formula for the area of ​​an equilateral triangle is (sqrt(3)/4)*a², where a is the side length. Substituting a=19, we get:

Area of ​​base = (√(3)/4)*19²

= 207.39 mm²

Then we find the area of ​​one triangular surface. We can use the formula for the area of ​​a triangle, which is (1/2) the height of the base. The base of the triangle is the other side of an equilateral triangle with a length of 19 mm. The height of the triangle is the  height of the diagonal of the pyramid, which is 17 mm. Using the Pythagorean theorem, we can find the length of the height of the triangle:

h = √ (slope² - (1/2 base)²)

= √(17² - (1/219)²)

= 15.27 mm

Thus, the area of ​​one triangular surface is:

Area of ​​triangle = (1/2)1915.27

= 144.97 mm²

Since there are four triangular faces, the total area of ​​the triangular faces is:

Total area of ​​triangular surfaces = 4 × 144.97

= 579.88 mm²

Finally, the  area of ​​the pyramid is the sum of the area of ​​the base and the area of ​​the four triangular sides:

Area = area  of ​​base Total area of ​​triangular surfaces

= 207.39 + 579.88

= 787.27 mm²

Therefore the  area of ​​the triangular pyramid is 787.27 square millimeters.

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Answer:

(-5,-5)

Step-by-step explanation:

Answer:

The rates are not equivalent since Maria saves $0.50 more per month than Ralph.

Step-by-step explanation:

We can determine if two rates are equivalent by comparing the rates at which they save per month.

Maria's savings per month:

Both 50 and 4 can be divided by 2, which gives us 25/2.  As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.

Ralph's savings per month:

Both 60 and 5 can be divided by 5, which gives us 12.  Thus, Ralph saves $12 per month.

Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.

Answer:

Concept:

When encountering questions that ask for simplifying expressions through operation, following the PEMDAS method would be easier:

Therefore, the whole process of simplifying the given expression should follow the PEMDAS method. For extra, whenever there are two occurences of the same operation, then prioritize the leftmost and go right.

Hope this helps!! :)

Please let me know if you have any questions or need further explanation

Step-by-step explanation:

w = width

2w + 2 =  Length

Area = W x L  = 84 = w (2w+2)

                          84 = 2w^2 + 2w

                            0 = 2w^2 + 2w - 84        Use Quadratic Formula

                                                                 a = 2    b=2    c = -84

to find  

W = 6      then     L =  14 inches

Answer:

C.   y = 12m

as the year has 12 month then here the 12 should be set beside the (m) that represents the months.

The expression that models the number of people attending concert 1 is given as follows:

512/6.

The number of people attending concert 1 is obtained applying the proportions in the context of the problem.

From the bar model, the fractions corresponding to each concert are given as follows:

The total number of people is given as follows:

512.

Hence the expression that models the number of people attending concert 1 is given as follows:

512/6.

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THINGS TO REMEMBER:

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Question: Write an expression for how much it would cost to park for 3d hours on a holiday during peak hours.

-----

Answer: 3d × 2  or  3d + 3d

-----

Explanation: This is because during holidays the amount of d doubles. However since this is on a holiday DURING peak hours it would be 3d × 2

-----

Question 2: Then, if the basic off-hours parking rate is $2.50 per hour, how much would a person pay to park for 3d hours in the situation described above?

-----

Answer: $15

-----

Explanation: Since d represents dollars we would multiply 2.50 times 3 which would give us 7.5 then we double this since it is during holidays giving us $15

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NOTE: I AM SO SORRY IF THIS IS WRONG AND I MISSED SOMETHING. IF IT IS WRONG THEN PLEASE MAKE SURE TO TELL ME SO I CAN FIGURE OUT WHAT I MISUNDERSTOOD

Again I'm sorry but I hope I helped a little bit.    

Answer:

1. 48x+6

2.36+48x

3.48x+32

4.36+48x

I think it will help you.

Answer:

4080

Step-by-step explanation: