factorise fully 8x^2-4x

Answer:

Raymond

Step-by-step explanation:

1 ) Eve and Patty swam fewer laps than Maureen so...

Eve and Patty < Maureen

2 ) Patty swam more laps than Eve...

Patty > Eve

3 ) Maureen swam fewer laps than Raymond...

Maureen < Raymond

4 ) We can eliminate Eve and Patty since they swam fewer laps than Maureen. The ones who are left are...

Maureen and Raymond

5 ) We know that Maureen swam fewer laps than Raymond so we can eliminate Maureen.

Raymond

6 ) This mean that the one who swam the most laps is...

Raymond

Hope this helps! :)

Answer:

1.5 liters

Step-by-step explanation:

The third term of F(n)=3n-4 is 5.

Two or more expressions with an Equal sign is called as Equation.

Given,

F(n)=3n-4

F of n equal to three times of n minus four.

We need to find the third term.

To find third term we need to plug 3 in place of n.

F(3)=3(3)-4

Three times three minus four

F(3)=9-4

Nine minus four gives 5

F(3)=5

Hence, the third term of F(n)=3n-4 is 5.

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The interest on the borrowed amount after 7 years is $486.

The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.

Given that,

The amount borrowed is  P = $200.

Rate of interest is r = 18% per annum compounded quarterly.

Total time is t = 7 years

Then, the rate of interest for quarterly compounding is given by,

r  = 18 / 4%

  = 4.5%

And, total time period for compounding is,

n = 7 × 4

  = 28

The formula for compound interest is given as,

P[(1 + r / 100)ⁿ - 1]

Substitute the respective values to get,

200 × [(1 + 4.5 / 100)²⁸ - 1]

= 200 × 2.43

= 486

Hence, the interest due on the loan is given as $486.

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The equation Damian can use to found out how much money he still owes is -

y = - 43x + 774  

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have the following problem -

Damian bought a new game station for $774 using the stores zero interest finance plan. He will pay $43 a month for 18 months.

We can represent the equation he can use to found out how much money he still owes using a straight line as follows -

y = 774 - 43x

y = - 43x + 774              [x] is the number of month

Therefore, the equation Damian can use to found out how much money he still owes is -

y = - 43x + 774  

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Answer:

9.8 * 100 = 980

0.040 * 1000 = 40

61 / 10 = 6.1

8.909 * 100 = 890.9

Step-by-step explanation:

Answer:

x= 68  z= 180  y=38

Step-by-step explanation:

Answer:

Step-by-step explanation:

Equation of circle is, (x-h)^2+ (y-k)^2=r .......(eqn1)

where, (h,k) is the center and r is the radius.

therefore, from the question by rearranging the equation,

x² + y² + 4x − 6y + 12=0

viz, (x² +4x+4) + (y²-6y+9)-1=0  

(x+2)^2 + (y-3)^2=1

therefore from eqn1, (-2,3) is the center and radius is 1

The standard score (z-score) of the given sample mean is equal to 7.11

A standard score is also referred to as a z-value or z-score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

Mathematically, the standard score of a given sample mean can be calculated by using this formula:

[tex]Z=\frac{\bar{x}\;-\;\mu}{ \frac{\delta}{n} }[/tex]

Where:

Where:

Substituting the given parameters into the formula, we have;

Standard score, z = (30 - 31)/(9/64)

Standard score, z = -1/0.140625

Standard score, z = 7.11

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The future value of the annuity investment is expressed in option A

The future value formula is used to calculate the future value (FV) of an investment with given inputs of compounding periods (N), interest/yield rate (I/Y), starting amount, and periodic deposit/annuity payment per period (PMT).

The formula can be expressed as

FV = [MP(1 + r/n)^nt - 1] / [r/n]

We can substitute the values into the equation;

FV = 250[(1 + 0.062/12)^12 * 30] / 0.062 /12

The answer to this question is option A

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Answer:

195312

Step-by-step explanation:

Using the formula for the sum of a geometric sequence,

[tex]\frac{2(1-(5)^8)}{1-5}=195312[/tex]

Answer: X

Step-by-step explanation:

you just start at 0 since that is the origin and go up 5

Answer: 3.28 inches

Step-by-step explanation:

Fabric used for players and coaches is 776.32 inches.

Number of players is 29 and coaches is 3

So fabric used for each player and coach for the headbands is

776.32/29+3 = 24.26 inches

So, for the players 24.26 of fabric will be used for the headbands.

Total fabric used for the wristbands is 247.66 inches

Fabric used for the wristband is

247.66/29 = 8.54 inches

So, total amount of fabric used by Shelia for the wristband and headband is 24.26 + 8.54 = 32.8 inches.

The required percentage of height of 34 and 54 inches are 85% and 135%.

Given that,
The percentage of the height of 34 inches and 54 inches against the height of 40 inches is to be determined.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,

a,
percentage = 34/40 × 100%
Percentage = 85%

b,
percentage = 54/40 × 100%
Percentage = 135%

Thus, the required percentages of height of 34 and 54 inches are 85% and 135%.

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The linear equation in the slope-intercept is:

y = (-1/5)*x  - 26/5

And it can be written as:

y = (-1/5)*(x + 1) - 5

We can write the equation for line L as:

y = a*x +b

Where a is the slope and b is the y-intercept.

Two lines are perpendicular if the product between the slopes is equal to -1.

So if we want our line to be perpendicular to y= 5x, then we must have:

a*5 = -1

a = -1/5

So our line is something like:

y = (-1/5)*x + b

And the line passes through (-1, -5), replacing these values:

-5 = (-1/5)*-1 + b

-5 = 1/5 + b

-5 - 1/5 = b

-26/5 = b

The linear equation is:

y = (-1/5)*x  - 26/5

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The value of c by using the mean value theorem is c = 6.25.

The mean value theorem in mathematics says that for any given planar arc between two endpoints, there exists at least one point where the tangent to the arc is parallel to the secant between its endpoints. It is one of the most significant findings in the real-world analysis.

Given that the function is f(x) = 5√x and the interval is (4,9).

Calculate the value of 'c' as below,

f(x) = 5√x

f(4) = 5√4 = 10

f(9) = 5√9 = 15

Calculate the value of f'(c) as below,

f'(c) = ( f(b) - f(a) ) / (b - a)

f'(c) = f(9) - f(4) / ( 9 - 4 )

f'(c) = (15 - 10 )  / ( 9 - 4)

f'(c) = 1

Again the value of f'(x) is,

f'(x) = 5/2/√x

f'(c) = 5 / 2 / (√c)

5 / 2 / (√c) = 1

√c = 5 / 2

c = 25 / 4

c = 6.25

Therefore, the value of c by using the mean value theorem is c = 6.25.

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An equilateral triangle in geometry is a triangle with three equal-length sides. An equilateral triangle has congruent sides, which means that each side is the same length. The triangle MDE is equilateral only because it is midpoint of ACB

If the square of the longest side is smaller than the sum of the squares of the two smaller sides, the triangle is said to have an acute angle according to Pythagoras's theorem. Given a triangle with sides "a," "b," and "c," with side "a" being the longest, the triangle is steeply angled if "a2" exceeds "b2" plus "c2."

By adding the squares of the triangle's two smaller sides and comparing the result to the square of the largest side, you may determine whether the triangle is acute, right, or obtuse. The triangle is sharp because this total is higher.

Isosceles, equilateral, or scalene acute triangles are all possible. An acute triangle's longest side is located across from its biggest angle.

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If lliot and Jack share some money in the ratio . 8:5 Elliot got £21 more than Jack. The amount that Elliot received is £56.

Given data;

Sharing ratio 8:5

Amount Elliot got = 21

In order to determine  the amount that Elliot received we need to formulate and equation and then use the formulated equation to find the amount received.

Equation

21 × 8 ÷ (8-5)

Hence,

£21 × 8 ÷ (8-5)

£168 ÷ 3

=  £56

Therefore Elliot received £56.

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Answer:

B is never true

Step-by-step explanation:

you can't get a negative number when you have a even power

The length of the straw fitted in the box is 10.67 inches.

A cuboid is a solid three-dimensional object which has six faces that are rectangular with eight vertices, and twelve edges.

Given that, a straw is placed inside a rectangular box that is 5 inches by 5 inches by 8 inches, the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner,

Diagonal of a cuboid  = √ l² + w² + h²

Therefore, diagonal of the box = √ 5² + 5² + 8² = 10.67 in

Hence, The length of the straw fitted in the box is 10.67 inches.

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The correlation coefficient that is most likely to match a line of best fit of the form y = mx + b for this situation is of:

0.9.

The correlation coefficient is an index that measures correlation between two variables, assuming numeric values between -1 and 1.

If the correlation coefficient is positive, the relation is positive, that is, they are direct proportional. If the correlation coefficient is negative, they are inverse proportional.

If the absolute value of the correlation coefficient is greater than 0.6, the relationship between the two variables is classified as strong.

In the context of this problem, the variables are listed as follows:

The total price increases with the number of bananas bought, and there is a strong positive relationship between these two variables, hence the coefficient should be greater than 0.6 and the correct option is:

0.9.

The problem is given by the image shown at the end of the answer.

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The required value of x is 3 in the given equilateral triangle.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

The triangle given in the figure is an equilateral triangle.

We know that all sides are equal in the equilateral triangle.

As per the given figure,

side AB = side AC

6x - 3 = 3x + 6

6x - 3x = 6 + 3

Apply the arithmetic operation,

3x = 9

x = 9/3

x = 3

Therefore, the required value of x is 3 in the given equilateral triangle.

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23.45 inches fabric was used on a headband and 9.64 inches fabric was used on a wristband for each player.

No. of players = 29

No. of coaches = 4

Total fabric used for headbands = 773.85 inches

Total no. of people for headbands = 29 + 4

                                                          = 33

Fabric used for headband for 1 person = 773.85/33

                                                                 = 23.45 inches

Total fabric used for wristbands = 279.56 inches

Total no. of people for wristbands = 29

Fabric used for headband for 1 person = 279.56/29

                                                                 = 9.64 inches

Hence, fabric for headband is 23.45 inches and for wristband is 9.64 inches.

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Answer:

The correct equation is t = 12.25h.

The probability that exactly two of the four live in elderly care facilities is; 0.244

The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.

The general formula of binomial probability distribution is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

where;

Px = the probability of exactly x events occurring.

x = the number of expected successful outcomes.

p is probability of success

n is sample size

We are given;

p = 72% = 0.72

n = 4

Thus;

P(X = 2) = 4C2 * (0.72)^(2) * (1 - 0.72)^(4 - 2)

P(X = 2) = 0.244

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The elevation at the lower end of a drain is 119.8 feet. For the second drain difference in feet will be 10.55 feet and in inches will be 126.6 inch.

The height above or below a fixed reference point, most frequently a reference geoid, which is a mathematical representation of the Earth's sea level as an equipotential gravitational surface, determines a location's elevation. A vertical surface is depicted in an elevation when viewed from a point perpendicular to the viewer's picture plane. You are looking at the front elevation, for instance, if you are standing directly in front of a building and viewing its front. The height between a point and a horizontal surface is known as HEIGHT. The height of a point above (or below) sea level is known as its ELEVATION.

Here,

a. The length of drain= 52 feet

the gradual decrease=0.125 ft

elevation at high end=126.30 feet

elevation at low end,

=126.3-(52*0.125)

=126.3-6.5

=119.8 feet

b. The elevation at one end=94.67 feet

The elevation at other end=84.12 feet

The difference in elevation,

=94.67-84.12

=10.55 feet

=10.55*12

=126.6 inches

The elevation of a drain's lower end is 119.8 feet. The second drain will differ by 10.55 feet in feet and 126.6 inches in inches.

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Answer:

1

2

[

x

2

2

−

x

3

3

]

2

0

=

1

2

[

(

4

2

−

8

3

)

−

(

0

)

]

=

1

2

(

−

2

3

)

=

−

1

3

Step-by-step explanation: