Kimberley is taking part in a race. For the first 160 m she runs at 4 m/s. The remaining 420 m of the race takes her 120 seconds. What is Kimberley's average speed, in m/s, over the whole race? If your answer is a decimal, give it to 2 d.p.​

Answer:

$142.2

Step-by-step explanation:

First we know that we have $112

Then we calculate 112+27% and we get 142.24

Round that up and you get $142.2

Answer:

< is angle, Dont be confused

m<1= 51

m<2=39

m<3=90

m<4=51

m<5= 17

m<6= 129

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Answer:

5.86 lbs

Step-by-step explanation:

6.93 - 1.07 = 5.86

You subtract the weight of the basket from the weight of the basket full of apples to get the weight of just the apples

On solving the provided question, we can say that the value of the ellipse from give data will be = 4/9 + 9/36 = OD. (-2,4±3√3)

In mathematics, an ellipse is a planar curve that encompasses two focus points and ensures that the sum of the two distances from any point on the curve to the focal points is constant. In doing so, the circle—a particular variety of ellipse with two equal focus points—is generalized. The ellipse, whose eccentricity is less than 1, indicates the area containing the points whose distances from its two foci add up to a certain amount. Running tracks in sporting arenas and 2D egg forms are two straightforward examples of ellipses in daily life.

[tex](x+2)^2/9 + (y-4)^2/ 36 = 1[/tex]

x = 0 and y = 1

4/9 + 9/36

OD. (-2,4±3√3)

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The number of terms in the given expression "7x² +5x -5" is three terms .

An Algebraic Expression is defined as the expression that contains combination of constants and variables joined by mathematical operators .

For Example ; 2x + 3y .

The given Algebraic Expression is 7x² +5x -5 ;

we can see that the terms joined by the mathematical operators + and - ;

the given expression cannot be simplified further ,

So ,the first term is 7x² ;

the second term is 5x and the third term is 5 .

Therefore , the expression 7x² +5x -5 has three terms .

The given question is incomplete , the complete question is

How many terms are there in the expression 7x²+5x -5 ?

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There are three terms in the expression 7x² 5x 5.

The expression 7x² 5x 5 contains three terms. The first term is 7x² which is the product of 7 and x². The second term is 5x which is the product of 5 and x. The third term is 5 which is a constant term. All together, these three terms make up the expression 7x² 5x 5. The 7x² term is a quadratic term, since it contains a squared variable, while the 5x and 5 terms are linear terms, since they only contain a single variable. When these three terms are combined, the expression 7x² 5x 5 is formed.

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Answer: -4(a+3)

Step-by-step explanation:

You can take out -4 from -4 and -12

Answer:

-4(a+3)

Step-by-step explanation:

Right on edge!

For f'(a) is given by f'(a) = 6a + 2 and equation of the line tangent to the graph is y = -10x - 12.

f(x) = 3x² + 2x

f'(x) = 6x + 2

So f'(a) = f'(-2) = -12+2 = -10

In order to find tangent line , we need a slope and a point. We have the x-co-ordinate for our point, so we can plug that in to find Y-coordinate.

F(-2) = 8

The slope of tangent line is the derivative at this point  , f'(-2) = -10

Equation of line tangent,

y - 8 = -10(x - (-2))

y = -10x - 12.

The limit of a function in mathematics is a key idea in calculus and analysis regarding the behavior of that function close to a specific input.

Informally, a function f gives each input x an output f(x). If f(x) approaches L as x approaches input p, we say that the function has a limit L at that location. More specifically, any input that is sufficiently close to p when f is applied forces the output value arbitrarily close to L.

The concept of limit is specifically used in the various definitions of continuity. Roughly speaking, a function is continuous if all of its limits agree with the values of the function. The term "limit" is also used in the definition of the mathematical term "derivative," which in one-variable calculus refers to the maximum value of the slope of secant lines on a function's graph.

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Answer:

$29.88

Step-by-step explanation:

We first would need to figure out what 20% of $37.35 is.

0.2 (or 0.20) × 37.35 = 7.47

This means that the discount price is $7.47

Now subtract that from the total.

37.35 - 7.47 = 29.88

Therefore, his total in dollars and cents after the discount and before tax is twenty-nine dollars and eighty-eight cents.

There are 28 numbers in total that are odd numbers greater than 500 with no digit being repeated.

First, there are 18 odd numbers with four digits, and all of them are greater than 500. To see that, starting from the end of the number, there are 3 options for the last digit, 3 for the second last, 2 for the second digit, and 1 for the first digit. Multiplying one gets 3*3*2*1=18.

Second, for numbers with 3 digits, in order to be greater than 500, it must start either with 5 or with 6. If it starts with 5, there are 2 options for the last digit and 2 options for the second digit.

Thus, there are 4 different numbers in this case. Finally, if it starts with 6, then there are 3 options for the last digit and 2 options for the second digit. Thus, there are 6 different numbers in this case.

Complete question: How many different odd numbers greater than 500 can be made using some or all of the digits 1,3,5 and 6 with no digit being repeated?

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As per the permutations, there as 36 three digit numbers that are greater than 500 and which are odd one also.

The term permutation in math is defined as the way of arranging objects or numbers in order.

Here we have given that we have to identify the 3 digit numbers greater than 500 are odd

Let us make three digit numbers 1st

Here we know that if we want odd number at end then one number from three numbers can come there so

=> 3P1

Then the rest of the two numbers don't matter so

Then it can be written as

=> 3P2

Then the overall combination is written as

=> 3P1 * 3P2=18

Here now let us make four digit numbers

Then the digit odd again and it can be written as

=> 3P1

Here also the rest of the order Doesn't matter so

then it can be written as

=> 3P3 =6

Then the four digit value is

=> 3p1 * 3p3= 18

Therefore, the overall count is written as

=> Overall = 18+18= 36

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If a man has a collection of stamps made up of 5 cent stamps and 8 cent stamps and there are three times as many 8 cent stamps as 5 cent stamps. The number of each stamp he have is: 5 cent stamp is 12, 8 cent stamp is 36.

Let x represent 5 cent =  0.05x + 0.08 = 3.48

Let y  represent 8 cent = 3x

Hence,

0.05x + 0.08(3x)= 3.48

0.05x + 0.24x = 3.58

Combine like terms

0.29x = 3.58

Divide both side by 0.29x

x = 3.58/0.29

x =12 (5 cent stamps)

Now let solve for y

y =3x

y =3(12)

y = 36 (8 cent stamps)

Therefore the number of each stamp he have is: 5 cent stamp is 12, 8 cent stamp is 36.

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The number of possible outcomes for each case is given as follows:

i) 64 outcomes.

ii) 6 outcomes.

The combination is composed by four digits, and each digit is independent of other digits, meaning that the Fundamental Counting Theorem is used to obtain the possible number of combinations.

The Theorem states that the total number of combinations is given by the multiplication of the number of outcomes for each digit.

For item i, as repetition is allowed, the first digit assumes a value of 1, hence there is only one possible outcome, while each of the remaining three digits can assume three values, hence the number of combinations is given as follows:

N = 4 x 4 x 4 = 4³ = 64 combinations.

When repetition is not allowed, and the number starts with the number one, we have that:

Hence the number of combinations is obtained as follows:

N = 1 x 3 x 2 x 1 = 6 combinations.

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Answer: The quarter

Step-by-step explanation:

The quarter is larger and there are more quarters than there are any other coins in her pocket.

The maximum possible outcome for the situation is 36.

The number of favorable events to all the events in an experiment is the ratio that makes up the probability formula. Theoretical probability, Experimental probability, and Axiomatic probability are the three categories into which probability can be divided.

We have been Given that Ruby is designing a new board game and is trying to figure out all the possible outcomes.

Ruby flips a coin, rolls a fair die in the shape of a cube that has six sides labeled 1 to 6, and spins a spinner with three equal-sized sections labeled Walk, Run, Stop.

we know that there are 3 things happening simultaneously and favorable moments will be chosen by all three.

Thus, Maximum possible outcome are;

2 x 6 x 3 = 36

Therefore, For the given, 36 outcomes are available in total.

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The trigonometric ratios are;

We know that the trigonometric ratios would have to do with the ratios such as the sine the cosine and the tangent of the angle. In This case, we would need to obtain the side AB and this is by the Pythagoras theorem;

/AB/^2 = /AC/^2 + /BC/^2

/AB/ = √ /AC/^2 + /BC/^2

/AB/ = √(9)^2 + (12)^2

/AB/ = 15

Then;

Sin A = 12/15

Cos A = 9/15

Tan A = 9/12

These are the ratios for the right angle triangle

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Answer:

w(n)= -20

Step-by-step explanation:

w(9)=-2(9)-2

= -18-2

=-20

Answer:

w(9) = -20

Step-by-step explanation:

w(n) = −2n – 2

w(9) = −2(9) – 2

w(9) = -18 - 2

w(9) = -20

Answer:

LMNO is a parallelogram in which bisectors of the angles L, M, N, and O intersect at P, Q, R, and S to form the quadrilateral PQRS. Hence the angle bisectors of a parallelogram form a rectangle as all the angles are right angles; we conclude that it IS RECTANGLE. Hence proved.

A. The coefficient of x^4y^{12} in the expansion of (-4x+2y)^{16} is -8192.

B. The coefficient of x^4y^8z^7 in the expansion of (-4x+2y-1z)^{19} is -134217728.

For the first question, we can use the binomial theorem to expand the expression. The binomial theorem states that

(a+b)^n = C(n,0)a^nb^0 + C(n,1)a^{n-1}b^1 + C(n,2)a^{n-2}b^2 + ... + C(n,n)a^0b^n

Where C(n,k) = n!/(k!(n-k)!)

Applying this to the given expression, we get:

(-4x+2y)^{16} = C(16,0)(-4x)^{16}(2y)^0 + C(16,1)(-4x)^{15}(2y)^1 + C(16,2)(-4x)^{14}(2y)^2 + ... + C(16,16)(-4x)^0(2y)^16

The coefficient of x^4y^{12} is the coefficient of the term -4x^42y^{12} in this expansion, which is

C(16,4)(-4)^42^{12} = C(16,4)(-256)4096 = C(16,4)(-256)*4096 = -8192

For the second question, the same logic can be applied to:

(-4x+2y-1z)^{19} = C(19,0)(-4x)^{19}(2y)^0(-1z)^0 + C(19,1)(-4x)^{18}(2y)^1(-1z)^0 + C(19,2)(-4x)^{17}(2y)^2(-1z)^1 + ... + C(19,19)(-4x)^0(2y)^0(-1z)^19

The coefficient of x^4y^8z^7 is the coefficient of the term -4x^42y^8(-1z)^7 in this expansion, which is C(19,4)(-4)^42^8*(-1)^7 = C(19,4)256256*-1 = -134217728

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Answer:

Step-by-step explanation:

The percentage of pink is 13%.

The solution is Option B.

The area of the triangle is A = 10 units which is one-half the area of a rectangle of length 4 units and width 5 units

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Let the coordinates of the triangle ABC be

The coordinate of A = A ( 4 , 6 )

The coordinate of B = B ( 6 , 1 )

The coordinate of C = C ( 2 , 1 )

Now , the base of the triangle B = 4 units

The height of the triangle H = 5 units

And , The area of the triangle = ( 1/2 ) x Length x Base

Substituting the values in the equation , we get

The area of the triangle = ( 1/2 ) x 4 x 5

The area of the triangle = 10 units

Now , one-half the area of a rectangle of length 4 units and width 5 units

Substituting the values in the equation , we get

Area of rectangle = ( 1/2 ) Length x Width

Area of rectangle = ( 1/2 ) 4 x 5

Area of rectangle = 10 units

Hence , the area of triangle is 10 units

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Answer:

Below

Step-by-step explanation:

x = third part

5/9 x    + 5/9 x  + x   = 114    <=======given

19/9  x = 114

x = 114 * 9/19 = 54 cm      then the other two are 30 cm each

Answer:

The two equal parts are 30 cm, the third part is 54 cm

Step-by-step explanation:

x =  third part

(5/9)x + (5/9)x + x = 114

10/9(x) + x = 114

(19/9)x = 114

x = 114(9/19) = 54

(5/9)54 = 30

Alex came closer to their grade’s state record for the triple jump.

What is algebra?

The area of mathematics known as algebra is used to help express issues or circumstances into mathematical expressions.

Here, we have

Given:

Alex jumped 38 feet 11 2/3 inches the eighth-grade record is 40.17 feet.

Let's see how closer Alex jumped.

11 2/3 inches = 22* 0.083 = 1.826

38+ 1.826 = 39.826

40.17 -  39.826  = 0.344

Eric, a seventh grader, jumped 36.89 feet. The seventh-grade record is 38 feet 1 3/5 inches.

1 3/5 inches = 8/5*0.083 = 0.1328

38 + 0.1328 = 38.1328

Eric jump was

38.1328 - 36.89 = 1.2428

0.344 is smaller than 1.2428.

Hence, Alex came closer to their grade’s state record for the triple jump.

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Answer:

1/2x - 2 = Graph D, with the x intercept as 4, and the y intercept at

Answer:

D

Step-by-step explanation:

f(x) = mx + b

f(x) = 1/2 x - 2

m is the slope (1/2) and b is the y-intercept (b) -2.

Only graphs C and D cross the y axis at -2 .  That is the point (0, -2)

The slope is 1/2.  That means a rise of 1  space up and a run of 2 spaces left.

If you start at the point (0,-2) and go up 1 space and 2 spaces right, you end up back on the line at the point (4,0).

The measures of all unknown angles and side lengths of δpqr of m∠R = 50 degrees, PR ≈ 5.74 cm, after solving the Pythagorean theorem equation, and PQ ≈ 8.53 cm, after solving the Law of Cosines equation.

In order to determine the measures of all unknown angles and side lengths of ΔPQR, we can use the properties of a triangle. In particular, we can use the fact that the sum of the angles in a triangle is 180 degrees and the Pythagorean theorem.

You can use the above information to find the value of PR and PQ using trigonometric functions and/or squares.

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The question is -

Determine the measures of all unknown angles and side lengths of ΔPQR. Round side lengths to the nearest hundredth.

m∠R =

PR ≈

PQ ≈

By adding all the distances of the branches, we will conclude that Sylvester traveled a distance of 66.74 meters.

We know that Sylvester is a slug, and it travels for four branches, such that the length of each branch is:

To get the total distance that Sylvester travels, we just need to add these 4 numbers, then we will get:

Total distance = 9.01 m + 12.31m + 19.5m + 25.92m

Total distance = 66.74 meters.

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Option C. p= 1/6; a= 8 values for p and a will cause the function [tex]f(x) = Pa^x[/tex]  to be exponential growth.

An exponential growth function is a function in which the variable x is the exponent of the base. In the function, [tex]f(x) = Pa^x,[/tex] the variable x is the exponent and the constant a is the base. For the function to be an exponential growth function, the base must be greater than 1.

In option A, P=6 and a=1/8. The base is less than 1 (1/8 < 1) so this function is not an exponential growth function.

In option B, P=6 and a=1. The base is equal to 1, which is not greater than 1, so this function is not an exponential growth function.

In option C, P=1/6 and a=8. The base is greater than 1 (8 > 1) so this function is an exponential growth function.

In option D, P=1/6 and a=1/8. The base is less than 1 (1/8 < 1) so this function is not an exponential growth function.

Therefore, the only option that causes the function [tex]f(x) = Pa^x,[/tex] to be an exponential growth function is option C. P=1/6; a=8.

Complete Question:

Which of these values for P and a will cause the function  [tex]f(x) = Pa^x[/tex]  to be an exponential growth function?

A. P=6; a = 1/8

B. P = 6; a = 1

C. P= 1/6; a=8

D. p= 1/6; a= 1/8​

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P= 1/6; a=8

Is a exponential growth function, because a > 1 and P is not zero

Now, According to the question:

We know that

The equation of a exponential growth function is given by:

[tex]f(x)=pa^x[/tex]

where

P is the initial value or y-intercept (this vale cannot be equal to zero)

a is the base of the exponential function ( in a exponential growth function the value of a is greater than 1)

Verify each case

case A) P=6; a = 1/8

Is not a exponential growth function, because a < 1 (is a decay exponential function)

case B) P=6; a = 1

Is not a exponential function

case C) P= 1/6; a=8

Is a exponential growth function, because a > 1 and P is not zero

case D) P=1/6; a = 1/8

Is not a exponential growth function, because a < 1 (is a decay exponential function)

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The complete question is this:

Which of these values for P and a will cause the function f(x) = Pa^x to be an exponential growth function?

A. P=6; a = 1/8

B. P = 6; a = 1

C . P= 1/6; a=8

D. p= 1/6; a= 1/8​

All the measures of central tendency are, The median, The mode, and The mean.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are some measures,

A. The median

B. A sample statistic

C. The mode

D. The lowest value

E. The mean

We know that;

The four measures of central tendency are mean, median, mode and the midrange.

Here, mid-range or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set.

Hence, All the measures of central tendency are, The median, The mode, and The mean.

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Answer: nomial  data

Step-by-step explanation:

Answer: below :)

Step-by-step explanation:

1. Line AB

2. Ray AB

3. Line segment AB

4. Ray BA

Brenna would take 20 min to cut the same wood into sixths.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let x be the rate at which Brenna cuts the wood in a single piece,
So, She can cut a log into thirds in 10 min.
x = 3/10

x = 0.3 cuts per minute for single wood,

Now,
time took to cut the same wood into 6 pieces
= 6 / x
= 6 / 0.3
= 20 min

Thus, Brenna would take 20 min to cut the same wood into sixths.

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