katie has £1200. she gives 1/3 of the money to her sister. Then katie give 1/4 of the remaining money to her brother. how much money does katie have left?

The function f(x)  = [tex]-x^2 + 3x +11[/tex] of the value is 7.

Given,

In the question:

The function is given as:

f(x) = [tex]-x^2 + 3x +11[/tex]

To find the f(-1)

Now, According to the question:

The function is :

f(x) = [tex]-x^2 + 3x +11[/tex]

To put the value of x = -1 in above function's equation:

f(x) = [tex]-x^2 + 3x +11[/tex]

f(-1) = [tex]- (-1)^2 + 3(-1) +11[/tex]

Solve the equation:

Determine the sign:

f(-1) = -1 -3 +11

Calculate the sum or difference:

f(-1) =7

Hence, The function f(x)  = [tex]-x^2 + 3x +11[/tex] of the value is 7.

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Answer:

Let h = number of hours.

[tex]20 + 5h = 10 + 10h[/tex]

[tex]4 + h = 2 + 2h[/tex]

[tex]4 = 2 + h[/tex]

[tex]h = 2[/tex]

In 2 hours, we will have the same amount of money.

the probability that the mean tire pressure of the sample is less than 69 psi 0.2030

The formula of the z-score is z = (x - μ)/σ, where

x is the score

μ is the mean

σ is the standard deviation

given,

a mean of 70 pounds per square inch

μ = 70

the standard deviation of 1.2 psi.

σ = 1.2

the sample is less than 69

x=69

so on substituting

z=(69-70)/1.2

z=-1/1.2

z=-0.83

The value corresponding to the z score is 0.2030 i.e 20.30%

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Answer:

false

Step-by-step explanation:

question 4

0. 25 points

if py increases to 6 the vertical intercept will be the same and the slope will be steeper

Answer:1 3/5

Step-by-step explanation:

All you have to do is we take quotient 1 as a whole part and in the fractional part remainder 1 as the numerator, and divisor 5 as the denominator.

Answer:1 3/5

Step-by-step explanation: 8/5-5/5= 3/5 so that leaves you with 1 3/5

The first mechanic worked 20 hours and the second mechanic worked 5 hours

The work charge of first mechanic = $115 per hour

The  work charge of second mechanic = $55 per hours

Total number of hours they worked = 25 hours

The total amount they charged = $2575

Consider the number of hours that first mechanic work as x and second mechanic as y

Then the equations will be

x + y = 25

x = 25 -y

The second equation

115x + 55y = 2575

Here we have to use substitution method here

115(25-y) + 55y = 2575

2875 - 115y +55y = 2575

2875 -60y = 2575

60y = 2875 - 2575

60y = 300

y = 300 / 60

y = 5 hours

Then x = 25 - y

= 25 -5

= 20 hours

Hence, the first mechanic worked 20 hours and the second mechanic worked 5 hours

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Answer:

y = 4x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

here m = 4 , then

y = 4x + c ← is the partial equation

to find c substitute (2, 9 ) into the partial equation

9 = 8 + c ⇒ c = 9 - 8 = 1

y = 4x + 1 ← equation of line

If an urn contains two red balls and three white balls and a ball is chosen at random, then the probability of getting white ball is 3/5

The number of red balls = 2 balls

The number of white balls = 3 balls

Total number of balls = 2 + 3

= 5 balls

The probability = Number of favorable outcomes / Total number of outcomes

Number of favorable outcomes = Number of white balls = 3

Total number of outcomes = 5

The probability = 3/5

Hence, if an urn contains two red balls and three white balls and a ball is chosen at random, then the probability of getting white is 3/5

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The  probability of getting face card in all 4 attempts is 0.0018 approximately.

What are face cards?

Any of the twelve cards in a deck with an image of a face on it is referred to as a face card. King, Queen, and Jack are the face cards in this deck.

Main Body:

Jack, Queen, and King are face cards, each of the four suits has one of each, so 12 face cards.

12/52 is the chance that the first one will be a face card.

Then it’s 11/51, 10/50, and 9/49.

And the chance for all four is thus all four multiplied together.

(12 / 52) * (11 / 51) * (10 / 50) * (9 / 49) = 0.001828

Hence the probability of getting face card on all attempt is 0.0018

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Answer:

19 1/4

Step-by-step explanation:

1 3/4 × 11 = 7/4 × 11/1 = 77/4 = 19 1/4

The number she divides the 1572 and got an answer of 104, the remainder of 12 is 15.

It is the basic arithmetic operation, in which you are separating the number into some parts.

Given:

The dividend = 1572,

The quotient = 104,

The reminder = 12

Calculate the divisor by the following formula,

Dividend = Divisor × quotient + Reminder

Substitute the values,

1572 = Divisor × 104 +12

Divisor = 15

Therefore, the number she divides the 1572 and got an answer of 104, the remainder of 12 is 15.

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If the side lengths of the state flag of Michigan are in the ratio 4:7. when the flag is 28 feet long the height will be 49 feet

The height of the flag is calculated using the scale factors,  4 : 7

if 4 is equivalent to 28 what would 7 be

4 / 7 = 28 / ?

4 * ? = 7 * 28

? = 7 * 28 / 4

? = 49 feet

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If 1200 square centimeters of material is available to make a box with a square base and an open top,

The largest possible volume of the box is V = 4000cm^3.

We have 1200 cm^2 worth of material. This represents the surface area of a box with a square base and an open top.

the dimensions of the box.

Square base implies the length and width are the same.

Let x = length/width.

The box has a height as well.

Let h = height

the surface area ; S.

S = (area of base) + (area of 4 walls)

The area of the base is x^2

The area of one of the walls is length times height, or xh. Since there are 4 of them, it would be 4 times xh, or 4xh.

S = x^2 + 4xh

And we know that S = 1200cm^2, so

x^2 + 4xh = 1200

Let's solve for h.

4xh = 1200 - x^2

h = (1200 - x^2) / (4x)

we require the volume formula.

V = (length) x (width) x (height)

And we know all of these.

V = (x)(x)(h)

V = (x^2) h

putting h = (1200 - x^2) / (4x) in the formula

V = (x^2) ( 1200 - x^2)/(4x)

We get a cancellation,

V = x(1200 - x^2)/4

V = (1/4)x (1200 - x^2)

This will be our volume function, V(x).

V(x) = (1/4)(x)(1200 - x^2)

To maximize V(x), we must first take the derivative and then make it 0. Using the product rule (and ignoring the constant 1/4), we have

V'(x) = (1/4) [ (1200 - x^2) + (x)(-2x) ]

Simplify,

V'(x) = (1/4) [ 1200 - x^2 - 2x^2 ]

V'(x) = (1/4) [ 1200 - 3x^2 ]

V'(x) = (1/4) [ 3(400 - x^2) ]

V'(x) = (3/4) [ 400 - x^2 ]

To maximize, make V'(x) = 0, and solve for x.

0 = (3/4) [ 400 - x^2 ]

0 = 400 - x^2

x^2 = 400

x = +/- 20

Therefore,

x = { 20, -20 }

However, since x represents a dimension, it can never be negative, and we must discard the negative solution. That means

x = 20.

This tells us that the maximum volume occurs when x = 20. However, the question is asking WHAT the largest volume of the box is. Solving this is as simple as plugging x = 20 into our volume function, V(x).

V(x) = (1/4)(x)(1200 - x^2)

Therefore,

V(20) = (1/4) (20) (1200 - 20^2)

V(20) = (1/4) (20) (1200 - 400)

V(20) = (1/4) (20) (800)

V(20) = (20/4)(800)

V(20) = 5(800)

V = 4000cm^3

Hence the answer is, the largest possible volume of the box is V = 4000cm^3.

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The distance the plane traveled from point A to point B is 10952 feet approx.

To solve this we have to use the Pythagoras theorem.

Given that the plane is at a constant height which can be supposed as the perpendicular (i.e 5750 feet) for the triangle which the plane , ground and the makayla make.

Now when the plane is at the A point then the angle of the elevation is 16°, so the distance from the makayla the plane  is :

tanθ = P/B,

B(distance of makayla to plane on ground at point A) = P/tanθ ,

B = 5750 / tan 16°,

B = 5750/ 0.28;

B1 = 20535 feet approx

Similarly when the plane reach at the point B then the angle of the elevation is 31° then the distance from the makayla and the plane would be different, which will be :

tanθ = P/B,

B(distance of makayla to plane on ground at point B) = P/tanθ ,

B = 5750 / tan 31°

B = 5750 / 0.6

B2 = 9583 feet approx

now the distance traveled by the plane is B1 - B2 :

which is 20535  - 9583

10952 feet approx

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Answer:10483

Step-by-step explanation:

The train will travel for approximately 50 kilometres in 1 hours.

The train travels 1 kilometre in 1 minute 20 seconds.

At this rate the number of kilometres the train will travel in 1 hour can be calculated as follows;

Therefore, lets convert 1 minutes and 20 second to hours.

20 seconds = 0.333333 minutes

Hence,

60 minutes = 1 hour

1.33333 minutes = ?

cross multiply

time in hours = 1.3333 / 60

time in hours = 0.02222221666

Therefore,

0.02 hours = 1 km

1 hours = ?

number of kilometres the train will travel in 1 hours = 1 / 0.02 = 50 km

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Answer:

84 counters

Step-by-step explanation:

⅖ + ½ = 7/10

10 - 7 = 3

280 ÷ 10 × 3 = 84

Answer:

28

Step-by-step explanation:

1/2×280=140(red counters)

2/5×280=112(yellow counters)

140+112=252

280-252=28(green counters)

A. The bacteria sample that had a smaller initial population is;

Sample A; 100 bacteria.

B. The sample that was larger in the 5th week was;

Sample A; by 8,300.

An exponential function is defined by the general expression;

y = abˣ

where;

a is initial value.

b is rate of change.

For Sample A, the values of the above parameters are given as;

a = 100

b = 3

Thus, the exponential function is:

f(x) = 100(3)ˣ

In the 5th week, the population will be calculated as;

f(5) = 100 * 3⁵

f(5) = 24300.

For Sample B, the exponential function is expressed as:

g(x) = 500(2)ˣ

In the 5th week, the population will be;

g(5) = 500 * 2⁵

g(5) = 16000.

The difference of the larger population in Sample A and the smaller population in Sample B is;

24300 - 16000 = 8300.

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The probability of getting all heads when flipping a coin four times is 1/16.

(HHHH), (HHHT), (HHTH), (HHTT), (HTHH), (HTHT), (HTTH), (HTTT), (THHH), (THHT), (THTH), (THTT), (TTHH), (TTHT), (TTTH), (TTTT) are some examples of spaces.

There were 16 total outcomes.

Probability going out of control

HHHH P(A) = P(getting all heads) = 1/16

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Answer:

a =-13/24 b = 5/3

Step-by-step explanation:

From given

8a + 5b = 4 (1)

3b = 5 (2)

Using (2)

b = 5/3

Putting the value of b into (1) gives

8a + 5(5/3) =4

8a + 25/3 = 4

8a = 4 - 25/3

8a = -13/3

a = -13/(3*8)

a = -13/24

Answer:

Step-by-step explanation:

first up, the perimeter is 4 side added up. so we do 72/4= which equals 18. we need to apply the 6 to the sides so we do 6/2=3 18/3=15 f=15 18+3= 21 one side is 15 & the other side is 21 to double check, 21+15*2= 72

After simplifying the percentage, if 120% of a is equal to 80% of b, then a+b is 5.

In the given equation,

If 120% of a is equal to 80% of b, then we have to find the value of a+b.

We firstly express the statement in the algebraic equation.

It is given in the statement that 120% of a.

We write it as 120%×a.

From the statement, 80% of b.

We write its as 80%×b.

Both are equal to each other.

So the expression should be

120%×a=80%×b

Divide by 12% on both side

120%/120% ×a=80%/120% ×b

Simplifying

a=80%/120% ×b

As we know that % means 100 but both number 80 and 120 have % sign. So the % sign emitted.

So a=80/120 ×b

Divide by b on both side

a/b=80/120 ×b/b

a/b=80/120

Simplifying the ration

a/b=2/3

Hence, the value of a=2 and b=3.

Now finding the value of a+b.

a+b = 2+3

a+b = 5

Hence, if 120% of a is equal to 80% of b, then a+b is 5.

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Using midpoint theorem the value of DE is 4.

What is midpoint theorem?

 According to the midpoint theorem, "The line segment of a triangle linking the midpoint of its two sides is said to be parallel to its third side and is also half the length of the third side."

Here using midpoint theorem we know that ,

=> DE = 1/2 AB

Here DE=34-6x and AB=28-4x.

=> 34-6x=1/2(28-4x)

=>68-12x=28-4x

=> 12x-4x=68-28

=> 8x = 40

=> x =5.

Now put x=5 into DE then,

=> DE=34-6(5)=34-30 = 4.

Therefore using midpoint theorem value of DE is 4.

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The ratio of time that the red ball reaches the ground when compared with the green ball is 2:1

By using the equations of motion we first find the acceleration and time of both the balls using [tex]v^{2} -u^{2} =2as[/tex] and [tex]v=u+at[/tex]

where,

v=final velocity,

u=intial velocity,

a=acceleration,

s=height,

t=time

For the red ball,[tex]v^{2} -u^{2} =2as[/tex], v=4m/s, u=0m/s, s=3m by substitiuting in the equation we get ,

[tex]4^{2} -0^{2} =2*a*3[/tex],

acceleration=a=16/6=8/3,

[tex]v=u+at[/tex] by substituting we get,

4=0+8/3*t,

time taken by the red ball to reach ground t=3/2

For the green ball,[tex]v^{2} -u^{2} =2as[/tex], v=8m/s, u=0m/s, s=3m by substituting in the equation we get ,

[tex]8^{2} -0^{2} =2*a*3[/tex],

acceleration=a=64/6=32/3,

[tex]v=u+at[/tex] by substituting we get,

8=0+32/3*t,

time is taken by the green ball to reach ground t=3/4

and their ratio of time red ball/green ball=(3/2)/(3/4)=2/1,

hence time to reach the ground is independent of their mass

therefore, the ratio of time that the red ball reaches the ground when compared with the green ball is 2:1

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Answer:

8

Step-by-step explanation:

you divide so you can get the average

Answer:

in average she makes 8 friend in a week.

Step-by-step explanation:

You divide 80 by 9 that is 8 remaining 1, so yeah.

The given system of equations has no solution.

What is substitution method?

In order to solve a system of equations, the substitution approach is typically utilized in mathematics. The first equation involving the variable must be solved using this procedure before the variable's value is substituted in the second equation.

Consider, the given system of equations,

y + 7 = 3x          ..(1)

6x - 2y = 12             ..(2)

From equation (1),

y = 3x - 7.

Substitute value of (y) in inequation (2),

6x - 2(3x - 7) = 12

6x - 6x - 14 = 12

            -14 = 12

It is not possible to solve -14 = 12.

Therefore, the given system of equations has no solution.

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The length of the guys wire to the nearest foot is 56 feet.

The pole 5 ft tall is used to support the guy wire for the tower, which runs from the tower to a metal stake in the ground.

The situations forms a right angle triangle.

Therefore, the length of the guy wire can be found as follows:

Using trigonometric ratios, we can find the angle the guy wire made with the ground.

tan ∅ = opposite / adjacent

tan ∅ = 5 / 1

∅ = tan ⁻¹ 5

∅ = 78.690067526

∅ = 78.69°

Therefore, let's find the length of the guy wire using the angle.

cos 78.69° =  adjacent / hypotenuse

0.1961172908 = 11 / h

h = 11 / 0.1961172908

h = 56.088884361

Therefore,

length of the guy wire = 56 feet

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The cost ruler is £ 1.5 and the cost of rubber is £ 1.0.

Cost of 01 ruler be x pound.

Cost of 01 rubber be y pound.

according to question,

[tex]5x + 3y = 5.5[/tex]         ------------------------------------ (1)

[tex]3x + 2y = 3.5[/tex]         ------------------------------------(2)

multiplying equation (2) by 2 and equation (1)

[tex]10x + 6y = 11[/tex]       -------------------------------------(3)

[tex]9x + 6y = 10.5[/tex]      -------------------------------------(4)

subtracting equation (4) by (3), we get

[tex]x = 0.5[/tex]

putting the value of [tex]x = 0.5[/tex] in equation (2),

3×0.5 + 2y = 3.5

⇒1.5 +2y = 3.5

⇒2y= 2.0

⇒y = 1

∴ the cost of ruler is £ 0.5 and the cost of £1.0

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The inference rule is ({E and P} S1 {Q},{ not E and P} S2 {Q})/({P}if E then S1 else S2{Q}).

In the given question, we have to define the semantics (inference rule) of the if statement: {P} if (E) S1 else S2 {Q}.

A way of inferring the veracity of one assertion based on the significance of other assertions is known as an inference rule.

(S1, S2, ........, Sn)/S

According to the rule, if S1, S2,..., and Sn are real, then S's validity can be derived.

Given,

{P} if (E) S1 else S2 {Q}

The inference rule is

We know that if if E and P are true then it is S1 with postcondition {Q} or if E and P is false then it is else part that is S2 with postcondition {Q}

i.e. {E and P} S1 {Q},{not E and P} S2 {Q}

So the inference rule is:

({E and P} S1 {Q},{ not E and P} S2 {Q})/({P}if E then S1 else S2{Q})

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The value of x is 6.67 degrees.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

The (5x + 9)° angle on line m and the (7x -  9)° angle on line n are corresponding angles.

We have given that Line m and Line n are parallel.

t line is the transversal line on the two parallel lines, line m and line n.

We see that,

(5x + 9)° angle on line m is corresponding to the  (7x -  9)° angle on line n.

So,

(5x + 9)° +  (7x -  9)° = 180

12x = 180

x = 80 /12

x = 6.67

Thus, The value of x is 6.67 degrees.

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