in a car park cars can be parked in one row side by side. Fred marks the parking spaces with parallel lines 260cm apart. The row is 63 metres long. How many parking spaces can fred make in a row?

Answer:

1

A bag contains 7 red balls and 3 green balls. Two balls are taken from the bag. Find the probabilities that they are:

(a)

both red

(b)

both green

(c)

one red and one green.

Show me

2

Weather experts estimate the probability of rain any day as

0.6 if it rained the previous day

0.3 if it did not rain the previous day.

Find the probability that a dry day is followed by,

(a)

two more dry days,

(b)

two wet days,

(c)

a wet day and then a dry day.

Show me

Exercises

1

A bag contains 3 red counters and 4 blue counters. Two counters are taken out of the bag. Find the probability that:

(a)

both counters are red,

Check

(b)

both counters are the same colour,

Check

(c)

the counters are different colours.

Check

2

A card is drawn at random from a full pack of playing cards. It is not put back. A second card is then drawn from the same pack.

(a)

Find the probability that:

(i)

both cards are hearts,

Check

(ii)

only one card is a heart,

Check

(iii)

neither card is a heart.

Check

(b)

Find the probability that:

(i)

both cards are sevens,

Check

(ii)

neither card is a seven,

Check

(iii)

at least one seven is obtained.

Check

3

The probability that a football team win their next match is:

⎧

⎨

⎩

0.3 if they won their last match,

0.8 if they lost their last match.

(a)

Find the probability that if a match is lost, the next two will be won.

Check

(b)

Find the probability that if a match is won, the next two will also be won.

Check

4

A pack of 24 cards contains 12 red cars, 8 yellow cards and 4 pink cards. In a game a player has to select two cards, one after the another. Find the probabilities that a player selects,

(a)

2 red cards,

Check

(b)

2 yellow cards,

Check

(c)

2 pink cards,

Check

(d)

2 cards that are the same colour,

Check

(e)

a pink card and a yellow card in any order.

Check

5

Nisha buys a bag of sweets. The bag contains 3 orange, 17 strawberry and 10 cherry flavour sweets. Nisha eats 3 sweets. Find the probability that she has:

(a)

not eaten an orange sweet,

Check

(b)

eaten 3 sweets of the same flavour,

Check

(c)

only eaten strawberry flavour sweets.

Check

6

Two yachts A and B regularly race against each other. In rough weather the probability that A wins is 0.8 and in fine weather 0.4. The probability of fine weather at a race is 0.7.

(a)

What is the probability that A wins a race?

Check

(b)

If there is a best of 3 races competition, what is the probability that A wins the competition?

Round up to 2 decimal places.

Check

7

Brian enjoys swimming. If it is a sunny day the probability that he swims is 0.9. It the day is not sunny, the probability that he swims is 0.65.

The probability that tomorrow will be sunny is 0.8.

Draw a tree diagram to illustrate this information.

Calculate the probability that Brian will not swim tomorrow.

Check

8

Wes gives Bronwen a box of 25 mixed sweets. 12 of the sweets have soft centres, 8 have toffee centres and 5 have hard centres. All of the sweets have identical wrappers. Bronwen chooses 2 sweets at random.

(a)

What is the probability that Bronwen will choose 2 toffee centred sweets?

Check

After they have eaten 3 soft centred sweets and 2 toffee centred sweets, Wes chooses 3 sweets at random from the 20 sweets that are left.

(b)

What is the probability that Wes will choose a soft centred sweet, followed by a toffee centred sweet, followed by a hard centred sweet?

Check

When there are only 10 sweets left, 3 have soft centres, 4 have toffee centres and 3 have hard centres. Bronwen chooses two sweets at random.

(c)

What is the probability that neither of the sweets will have a hard centre?

Check

9

The fast food chain Macduff's is running a competition.

You obtain a card with 12 circles covered up.

You are allowed to scratch off up to three circles.

You win if 2 or more PALM TREES are revealed.

You lose if two or more CRABS are found.

If you win, you scratch off one of the three squares to show your prize.

Step-by-step explanation:

Answer:

m=y2-y1/x2-x1

=-4-5/-1-2

=-9/-3

=-3

The perimeter of the triangle ABC will be 54 units.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

In the diagram, AC is parallel to RP.

Then the triangle ABC and RBP will be similar.

Then the ratio of the corresponding sides will be constant.

BP / 10 = 7 / 14

      BP = 5

Then the perimeter of the triangle ABC will be

Perimeter = 7 + 14 + 18 + 10 + 5

Perimeter = 54 units

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Answer:

it can be written as 0.44y=40

44% can be written as 0.44

Step-by-step explanation:

to solve for y divide both sides by 0.44

to get y is equal to 100

Answer:

Yes

Step-by-step explanation:

She had more than me

I would help her but she has less than me

Step-by-step explanation:

This is a common knowledge of equivalent fractions.

Multiplying both the numerator and denominator of a fraction by the same quantity does not change the value of the fraction.

Not only multiplication, but division also works. What ever operation performed on the numerator must also be performed on the denominator.

1/2 = 2/4 = 4/8 = 16/32

The number of different positive four digit integers contain each of the digits 0, 1, 2, and 3 exactly once is 18

The given digits = 0, 1, 2 and 3

Total number of digits = 4

We need to create different four digit integers contain each of the digits 0, 1, 2  and 3 exactly once

Here we have to use the permutation

Here first number cannot be zero

Number of digits possible in thousands place = 3

Then different positive four digits integers = 3 × 3 × 2 × 1

= 18

Therefore, 18 different four digits numbers can be formed by using the given digits

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Answer:

Step-by-step explanation:

y=mx+b where m=slope and b=y intercept

m=(y2-y1)/(x2-x1), we have points (0,0) and (4,12)

m=(12-0)/(4-0)=12/4=3

y=3x+b, using point (4,12) we can solve for b

12=3(4)+b

12=12+b

b=0 so the line is

y=3x

By AAS property triangle, △BAD and △CDA are congruent.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

In the given figure,

∠ABD≅∠DCA,

BA perpendicular to AD,

And AD perpendicular to DC.

Since in Triangle, ABD ∠A is 90°,

And in triangle DCA angle ∠D is 90°,

Also,  ∠ABD≅∠DCA,

Implies that, ∠BDA = ∠CAD

By Angle-Angle-Side property,

△BAD and △CDA are congruent.

Hence, △BAD≅△CDA.

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1. If you have collected data on all persons living in the apartment building, it is considered a census. A census is a complete collection of data from every individual or unit in a population.

2. If you have collected data only on people who were home during your visits to the building, it is considered a sample. A sample is a subset of the population from which data is collected. In this case, it would be a convenience sample, as you are only collecting data from those who happened to be present during your visits.

3. If you asked people to give their age and collected it as age categories (e.g., <5, 6-10, 11-15, etc.), this is an example of a categorical variable. Categorical variables are qualitative and represent characteristics or attributes that fall into distinct categories or groups.

4. If you asked people to give their ages in years, this is an example of a continuous variable. Continuous variables are quantitative and can take any numerical value within a certain range. Age in years can be measured on a continuous scale.

5. If you found that apartments with older water heaters had worse health outcomes, this would be considered observational evidence. It suggests a correlation between the age of water heaters and health outcomes, but it does not prove a causal relationship. Further research would be needed to establish causality.

6. If you observed that health was getting worse throughout your visits, this would also be considered observational evidence. It indicates a trend or pattern, but again, it does not prove causation. Other factors could be influencing the observed change in health.

7. If you found differences in health outcomes by age, this would be considered associative evidence. It suggests a relationship between age and health outcomes, but it does not imply causality. Other factors could be influencing the observed differences.

8. If you found that younger people in the building had worse outcomes and offered an intervention to help improve their health, the decision would be supported by associative evidence. The observed association between age and health outcomes suggests that targeting younger individuals with interventions may be beneficial. However, further research would be needed to confirm the effectiveness of the intervention.

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Answer:

32

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

We have shown that for any two elements x and y in G, xy = yx, and hence, G is abelian.

The key step in the proof was the left-right cancellation property of G, which allowed us to substitute xy for zx and obtain x = y. This property implies that the group is abelian, and hence, all elements commute with each other.

To prove that the group G is abelian, we need to show that for any two elements x and y in G, xy = yx.

Let x and y be any elements of G. Consider the element z = xy. Then, we have:

xy = zx

Multiplying both sides by y^-1, we get:

x = zy^-1

Now consider the element w = yx. Then, we have:

yx = zw

Multiplying both sides by y^-1, we get:

x = zy^-1

Since z = xy, we can substitute it in the above equation:

x = xy y^-1

Simplifying, we get:

x = y.

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G is an abelian group since the commutative property holds for any elements x and y in G.

To prove that g is abelian, we need to show that for any x or y in the group g, we have xy = yx.

Let's take x and y in g. By the property given, we know that xy = xz implies y = z for any z in g.

Now let's consider the products xy and yx. We have:

xy * yx = x(yy)x (associativity of the group operation)
      = x(y^2)x

Let z = y^2 in the property given. Then we have:

xy * yx = x(y^2)x implies y2 = yx.

Using the same property again with z = x, we have:

yx * xy = y(x^2)y implies x2 = xy.

Multiplying the two equations, we get:

y2x2 = xyxy

Since the group operation is associative, we can also write this as:

(yx)^2 = xyxy

But we just showed that y2 = yx and x2 = xy, so we can substitute and simplify:

(yx)2 = xyxy
      = y^2x^2
      = (yx)(xy)
Compute x(xy) and (xy)x:

x (xy) = (xx)y = ey (since xx = e, the identity element)
(xy)x = y (xx) = y (since xx = e)

So, ey = y = yx, which implies that xy = yx for any elements x and y in G. Cancelling (yx) on both sides, we get:

yx = xy

Therefore, G is an abelian group since the commutative property holds for any elements x and y in G.

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Answer:

15

Step-by-step explanation:

21-6=15

Answer:

The answer is 15

Step-by-step explanation:

Just subtract

The required value of  polynomial is f(x) = x² - 35x + 219.

To find the smallest possible value of the polynomial f(x), we need to consider the smallest possible values for x. Given that f(7) = 23 and f(8) = 3, we can use these equations to form a system of equations.

Let's write the system of equations:
f(7) = 23, which means a(7²) + b(7) + c = 23
f(8) = 3, which means a(8²) + b(8) + c = 3

Simplifying these equations, we get:
49a + 7b + c = 23
64a + 8b + c = 3

To solve this system of equations, we can subtract the second equation from the first:
(49a + 7b + c) - (64a + 8b + c) = 23 - 3
49a - 64a + 7b - 8b = 20
-15a - b = 20

Now, we need to find the smallest possible value for a. Since a is an integer, we want the coefficient of a to be as small as possible. If we let a = 1, the coefficient becomes -15. This means that the absolute value of b will be minimized, resulting in the smallest possible value of the polynomial.

Plugging in a = 1 into the equation, we have:
-15(1) - b = 20
-15 - b = 20
-b = 20 + 15
-b = 35
b = -35

Now, we can substitute the values of a and b back into one of the original equations to find c:
a(7²) + b(7) + c = 23
(1)(49) + (-35)(7) + c = 23
49 - 245 + c = 23
-196 + c = 23
c = 23 + 196
c = 219

Therefore, the polynomial is f(x) = x²- 35x + 219.

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Answer:

so you need to divide this and turn it into a coefficient for the answer

Step-by-step explanation:

Answer:

m = -20

Step-by-step explanation:

7m - 4 - 9m - 36 = 0

Combine like terms

-2m -40 = 0

Add 40 to each side to isolate the variable

-2m  -40+ 40 = 0+40

-2m = 40

Divide each side by -2

-2m/-2 = 40/-2

m = -20

Answer:

f(0) = 3

Step-by-step explanation:

Step 1: Distribute

f(x) = -3x + 3

Step 2: Plug in

f(0) = -3(0) + 3

f(0) = 3

Answer:

f(0) = 3

Step-by-step explanation:

f(x) = -3(x-1)

Put x as 0 and solve.

f(0) = -3(0-1)

Solve the brackets.

f(0) = -3(-1)

Multiply both terms.

f(0) = 3

Answer:  The job pays $32,400 per year, and the agency fee is equal to 45% of one month's pay.

1. These points can be represented as ordered pairs: (0, f(0)) and (-1, f(-1)). 2. The function is concave up over the intervals (-∞, -1) and (0, +∞).

3. The function is concave down over the interval (-1, 0).

1. The points of inflection can be found by determining the sign changes in the second derivative of the function. Let's calculate the second derivative of f(x): f''(x) = 48x^2 + 48x. To find the points of inflection, we set f''(x) = 0 and solve for x. Setting 48x^2 + 48x = 0, we factor out 48x and obtain x(x + 1) = 0. So, the points of inflection occur at x = 0 and x = -1. These points can be represented as ordered pairs: (0, f(0)) and (-1, f(-1)).

2. The function is concave up when the second derivative, f''(x), is positive. To determine the intervals where f''(x) > 0, we consider the sign of the second derivative. Since f''(x) = 48x^2 + 48x, we find that f''(x) > 0 when x < -1 or x > 0. Therefore, the function is concave up over the intervals (-∞, -1) and (0, +∞).

3. The function is concave down when the second derivative, f''(x), is negative. To find the intervals where f''(x) < 0, we consider the sign of the second derivative. Since f''(x) = 48x^2 + 48x, we find that f''(x) < 0 when -1 < x < 0. Hence, the function is concave down over the interval (-1, 0).

In summary, the points of inflection for the function f(x) = 2x^4 + 8x^3 are (0, f(0)) and (-1, f(-1)). The function is concave up over the intervals (-∞, -1) and (0, +∞), and it is concave down over the interval (-1, 0).

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The p value for the difference is 0.005.

According to the statement

we have given that the 74 of 100 urban residents favor the construction while only 70 of 125 suburban residents are in favor.

And we have  to find the difference between them in proportions.

So,

X1 = 74 represent the number of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

X2 = 70 represent the number of people suburban residents are in favor

N1  = 100 sample 1 selected

N2 = 125 sample 2 selected

AND

P1 = 0.74 represent the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

And P2 = 0.56 represent the proportion of suburban residents are in favor And z would represent the statistic (variable of interest)  

Pv represent the value for the test (variable of interest)

Here we apply the Z test to find the difference then

Z = (0.74 - 0.56) / (0.64(1-0.64)(1/100+1/125) )^1/2

Now after solving

Z = 2.795.

Now The significance level provided is  ,and we can calculate the p value for this test.  

Since is a two tailed test the p value would be:  

P = (z>2,795)

P = 0.005.

So, The p value for the difference is 0.005.

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Answer:

The midpoint is (0,2)

Step-by-step explanation:

To find the x coordinate, average the x coordinates of the endpoints

(-4+4)/2 = 0/2 =0

To find the y coordinate, average the y coordinates of the endpoints

(6+-2)/2 = 4/2 =2

The midpoint is (0,2)

Answer:

Option b) Use the results from the 2014 survey.

Step-by-step explanation:

Using the results from the 2014 survey can reduce the sample size needed for the new survey, as it provides a good estimate of the population proportion. This reduces the margin of error and increases the confidence level of the new survey.

Answer:

The answer is A. -2/7

Step-by-step explanation:

Statement                Reason

m∠A ÷ 5 = m∠B       1. Given

m∠B = 20                 2. Given

m∠A ÷ 5 = 20           3. Substitution

m∠A = 100                4. Multiplication property of equality

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

m∠A ÷ 5 = m∠B  ____(1)

m∠B = 20 _____(2)

Substitute (2) in (1)

m∠A ÷ 5 = 20

m∠A / 5 = 20

Multiply 5 on both sides.

m∠A = 5 X 20

m∠A = 100

Thus,

Statement                Reason

m∠A ÷ 5 = m∠B       1. Given

m∠B = 20                 2. Given

m∠A ÷ 5 = 20           3. Substitution

m∠A = 100                4. Multiplication property of equality

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Answer:

74.8 cm^2

Step-by-step explanation:

The figure is a parallelogram with base of 11cm and height of 6.8cm . To find the area, we multiply the base by the height to get 11 × 6.8 = 74.8 cm^2

The required ratio of trombones to all the brass section members is 3 : 7.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Here,
The total number of members in the brass section of the jazz band is:

4 trumpets + 3 trombones = 7 members

The ratio of trombones to all the brass section members can be expressed as,

= 3 trombones / 7 brass section members

This ratio cannot be simplified further because the numbers are relatively prime.

Therefore, the ratio of trombones to all the brass section members is 3 : 7.

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The answer is 420.

Hope this helps ^^