19
Type A batteries and type B batteries were tested.
The cumulative frequency diagram shows information about the battery life of type A.
19 (a)
80
70
60
50
Cumulative
frequency 40
30
20
10
of
0
Type A
800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800
Battery life (hours)
Estimate the interquartile range for type A.
Answer
hours
[2 marks]

Answer:

(a)  3.5

(b)  x = 4

(c)  -¹/₂

(d)  -¹/₂

Step-by-step explanation:

f(1) is the value of y when x = 1.

To find the value of y from a given value of x, find the position of x on the x-axis, then trace vertically until you meet the line. Once you meet the line, trace horizontally to the y-axis to find the corresponding value of y.

Therefore, f(1) = 3.5.

To solve f(x) = 2, find the value of x when y = 2.

To find the value of x from a given value of y, find the position of y on the y-axis, then trace horizontally until you meet the line. Once you meet the line, trace vertically to the x-axis to find the corresponding value of x.

Therefore, the solution of f(x) = 2 is x = 4.

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Given interval:  2 ≤ x ≤ 4

Therefore:

[tex]\implies \dfrac{f(4)-f(2)}{4-2}=\dfrac{2-3}{4-2}=-\dfrac{1}{2}[/tex]

The average rate of change between any interval of the given function will be the same as the graph is linear.  Therefore, the average rate of change from 0 to 8 is the same as the rate found in part (c):  -¹/₂.

Proof

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Given interval:  0 ≤ x ≤ 8

Therefore:

[tex]\implies \dfrac{f(8)-f(0)}{8-0}=\dfrac{0-4}{8-0}=-\dfrac{4}{8}=-\dfrac{1}{2}[/tex]

Answer:

here's the answer

Step-by-step explanation:

the total calls are 39 call

the remaining calls are 1530

the remaining rounds are 481

481+39=520

520x3= 1560

The value of the lesser integer is 5

From the information given, we have the following deductions;

The expression can be represented as;

8(x + 1) - x = 43

expand the bracket, we have;

8x + 8 - x = 43

collect like terms

8x - x = 43 - 8

Subtract like terms

7x = 35

Make 'x the subject of formula

Divide both sides by 7

7x /7 = 35/7

x = 5

The lesser integer is x = 5

Thus, the value of the lesser integer is 5

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Answer: the time taken by train to cover 50km per hour is equal to the time taken by it to cover the distance of 250km for 5 hours

Step-by-step explanation:

You divide then together

Answer:

36 = 69

Step-by-step explanation:

45

Answer:

M is (-5,6)

N is (1,0)

P is (-4,2)

Step-by-step explanation:

We have to move all our coordinates in the same position and distance so we add and subtract the x and y values

M (-6,1) we add 1 to the x value and add 5 to the y value

M (-6+1,1+5)

So M prime is (-5,6 and we do that for the rest

Answer:

Here, I might have messed up one part , I think ;-;

Step-by-step explanation:

Answer:

An exponent is a power to a given number that will multiply the given number by itself the number of times the exponent's value represents. Exponents are represented by small, floating numbers that go after the given value in an equation.

Example A:

[tex]5^2 = 5 \times 5 = 25[/tex]

Example B:

[tex]x^4 + 8 = y[/tex]

Answer:

15.6 units (3 s.f.)

Step-by-step explanation:

The distance between 2 points is given by the formula below, where [tex](x_1, y_1)[/tex] is the first coordinate and [tex](x_2, y_2)[/tex] is the second coordinate.

[tex]\boxed{{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}[/tex]

Using the distance formula above,

distance between A(-3, 1) and B(7, 13)

= [tex]\sqrt{(13-1)^{2} + [7-(-3)]^{2} } }}[/tex]

= [tex]\sqrt{12^2+(7+3)^2}[/tex]

= [tex]\sqrt{244}[/tex]

= 15.6 units (3 s.f.)

Additional:

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Tom and Ben received 650 and 780 respectively.

Let the amount paid to each for every hour they work be x. Now, forming the equation as per the given information in question.

5x + 6x = 1430

Performing addition to find the value of x.

11x = 1430

Shifting 11 to Right Hand Side of the equation

x = 1430 ÷ 11

Performing division to find the value of x

x = 130

Now finding the amount received by Tom and Ben based on the number of hours they worked.

Amount received by Tom = 5x

Amount received by Tom = 5 × 130

Amount received by Tom = 650

Amount received by Ben = 6x

Amount received by Ben = 6 × 130

Amount received by Ben = 780

Therefore, the amount received by Tom and Ben are 650 and 780 respectively.

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John received $112.5 and Joan received $157.5 respectively as per the given ratio.

John and Joan share the amount in the ratio: 5:7

it is given that Joan had $45 more amount than John, therefore

Let the amount with John be x, so the amount with Joan will be x + 45

Formulating the equation we get:

Amount with John/Amount with Joan = Ratio of money with John/Ratio of money with Joan

x/(x + 45) = 5/7

7x = 5x + 225

2x = 225

x = 112.5

Amount with John  = 112.5

Amount with Joan = 157.5

So, amount John received $112.5 and Joan received $157.5 respectively.

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Answer:

6 units

Step-by-step explanation:
To find out how far apart two points are on a graph, we must count the spaces that separate them along the x and y axis

Counting on the x-axis, Point A is 2 units to the left of Point B

On the y-axis, Point A is 4 units below Point B.

Add the two to get the total units

Answer:

"Zero and its operation are first defined by [Hindu astronomer and mathematician] Brahmagupta in 628," said Gobets. He developed a symbol for zero: a dot underneath numbers.

Considering point Q (x, y) to be (1, 2), and translating it by (x-3, y+4), the image of point Q, say Q' will be positioned at (-2, 6), which is plotted in the reference image attached hereby.

As per the question statement, we are required to plot the image of point Q(x, y) under the translation (x-3, y+4).

Let us assume the point Q to be (1, 2). Therefore, a translation of (x-3, y+4) on (1 , 2) will result in a new position, which will be:

3 units to the left of (1, 2) along the x-axis, and then 4 units upwards along y-axis.

Hence, the position of the image of Q (1, 2) after a translation of (x-3, y+4) will be Q' [tex][(1-3), (2+4)]=(-2, 6)[/tex].

Both the points Q(1, 2) and its image after the translation of (x-3, y+4), Q'(-2, 6) are plotted in two separate graphs, attached hereby for reference.

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Answer:

14 1/2 fruits

Step-by-step explanation:

All of the coordinates in the attached screenshot are in the second quadrant.

Answer:

x=18

Step-by-step explanation:

it is a proportion

8:12=x:27

you have to multiply the know external terms(8 and 27) and divide them by the 12

Answer:

connect the last point to the first point to complete the question

translate the figure in part

translate the figure in part 3 units horizontal y and 6 units vertically

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

13, 15,17

Step-by-step explanation:

Let x = the first number

Let x + 2 = the second number

Let x + 4 = the third number

Consecutive means in order like 1,2,3 or 20,21,22. Consecutive odd means that you want three numbers in order that are odd.  Each number would be 2 more than the number before.  For example 5 + 2 = 7.  We would have to add 4 to 5 to find the next consecutive odd number.

x + (x + 2) + (x +4)  = 45  I put the numbers in parentheses so you could see the first number plus the second number plus the third number equals 45

x + x+ 2 + x+ 4 = 45  Combine like terms

3x + 6 = 45  Subtract 6 from both sides of the equation.

3x = 39  Divide both sides by 3

x = 13

Add 2 to that to get the next odd number.

Add 4 to 13 to get the third odd number.

Answer: 13 cm

Step-by-step explanation:

Let the value of the shortest of the three side lengths is x.

Since the three sides of a triangle are consecutive odd

integers, hence: x, x+2, x+4.

Thus,

[tex]P=x+(x+2)+(x+4)\\45=x+x+2+x+4\\45=3x+6\\45-6=3x+6-6\\39=3x\\[/tex]

Divide both parts of the equation by 3:

[tex]13\ cm=x[/tex]

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Work below. Enjoy!

- - - - - - - - - - - - - - - - - - - - - - - -

A simple way to determine the scale factor is to measure a segment's size in units and compare it to the original.

Segment XW = 6 units

Segment EF = 2 units

Now, simply divide the larger (6) by the smaller (2) and you get your answer (3).

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Good luck! :)

(Consider leaving a Brainliest if this helped!)
~pinetreee

Answer: 3.5

Step-by-step explanation:

A = 2, B = 7, C = 6

(7a + b)/c

=(7(2)+7)/(6)

=(14+7)/6

=21/6

=3.5

In the following ways we can break up the real numbers into the two disjoint subsets.

According to the given question.

We have to break the set of real numbers into two disjoint sets.

As we know that, two sets are said to be disjoint sets if they have no elements in common.

Therefore, in the following ways we can break up the real numbers into the two disjoint subsets.

The set of real numbers equal to zero and the set of other real numbers.

The set of natural numbers greater than 50 and the others. The set of real numbers whose absolute value is less than one, and the others. The set of real numbers whose square is less than 25 and others.

Like that we can break the set of real numbers into two disjoint subsets.

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Answer:

y=3x-8

Step-by-step explanation:

Slope -intercept form is y=mx+b.

M represents the slope; b represents the y-intercept.

First, let's find the y-intercept.

It'll be found on the y-axis on the graph.

If you go down the y-axis, you'll see that -8 is the only point to be directly on the y-axis, so we can assume that that's the y-intercept.

Thus, the B in the equation is -8.

Now, let's find the slope.

You can think of it as rise over run. The rise is how many numbers the y-intercept either goes up or down until it can cross over to the x-axis. Crossing sideways is the run that's located on the x-axis.

You can begin from -8 and either count downward or upward.

For the sake of this graph, we'll go upward.

Do you see the dot on the coordinate (1,-5)?

Count upward and go to the side to get to that coordinate.

I count three upward and one to the right.

So as a fraction that would be 3 over 1 or 3/1.

But you can simplify that to just 3.

Thus, the M in the equation is 3.

Hence, y=3x-8.

Hope this helps.

Answer:

3/25

Step-by-step explanation:

0.12 multiplied by 100 equals 12

which means 12/100 is 0.12

now simplify

6/50

3/25

Answer:-150

Step-by-step explanation:

Step 1: Solve all the integers.

−115-35

Step 2: Add the numbers and keep the negative sign.

-150

Hope this helps!!

P.S: It as a fraction is the same thing as it being in decimal from lol.

The coordinate of the midpoint of the segment with the given endpoints is (-1, 0)

The midpoint of a line is the point that divides the line into two equal parts.

The formula for calculating the midpoint is expressed as;

M(x, y) = (x₁+x₂/2, y₁+y₂/2)

Using the coordinate points (-6, 0) and (-4, 0)

M(x, y) = -6+(-4)/2

M(x, y) = -2/2

M(x, y) =-1

Hence the coordinate of the midpoint of the segment with the given endpoints is (-1, 0)

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Answer:

3 cans of tomato paste and 6 should be correct

No

Step-by-step explanation:

All numbers that are prime are odd and If the number is divisible by 2 it would be a composite number

The equation for Rhett's Situation is 70x + 50 = 250 and the equation for Scarlett's Situation is 70x + 35 = 250. In Rhett's case equation their is no expense per car wash but in case of Scarlett' equation their is expense of $5 per car wash.

Total amount earned by Rhett = $250  

Let the number of cars Rhett washed = x

Rhett charges $70 per car and earned $50 in tips. So, we can write

Total amount earned by Rhett = 70x + 50

On comparing total amount earned by Rhett, we get

70x + 50 = 250

The equation for Rhett's Situation is 70x + 50 = 250.

Total amount earned by Scarlett = $250  

Let the number of cars  Scarlett washed = x

Scarlett charges $75 per car wash and earned $35 in tips but also had to pay $5. 00 in cleaning supplies per car wash.. So, we can write

Total amount earned by Scarlett = 75x + 35 - 5x = 70x +35

On comparing total amount earned by Scarlett, we get

70x + 35 = 250

The equation for Scarlett's Situation is 70x + 35 = 250.

In Rhett's case equation their is no expense per car wash but in case of Scarlett' equation their is expense of $5 per car wash.

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Keiko used 83.5 pounds of type A coffee and 82.5 pounds of type B coffee in the blend.

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression

Given:

Type A coffee cost $5.35 per pound

Type B Coffee cost $4.05 per pound

Keiko made total 166 pound of the blend of $780.85

Therefore,

[tex]5.35x + 4.05y = 780.85 \;\;\;\;\; -------equation (1)[/tex]

[tex]x + y = 166 \;\;\;\; ---------equation (2)[/tex]

simplify the equation (2),

[tex]y = 166-x[/tex]

Substitute the value of y in equation (1),

[tex]5.35x + 4.05 (166-x) = 780.85[/tex]

[tex]5.35x + 672.3 - 4.05x = 780.85[/tex]

[tex]5.35x-4.05x=780.85-672.3[/tex]

[tex]1.3x=108.55[/tex]

Therefore,

[tex]Total\;pound\;of\;type\;A\;coffee\;is,\;x=83.5\;pounds[/tex]

Substitute the value of x in equation (2),

[tex]y=166-83.5[/tex]

Therefore,

[tex]Total\;pound\;of\;type\;B\;coffee\;is,\;y=82.5\;pounds[/tex]

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