A grocery shop sells apples and pears.
5 apples cost 60p.
8 pears cost 72p.
a) Work out the cost of 1 apple, in pence (p).
b) Work out the cost of 1 pear, in pence (p).
c) Which type of fruit is cheaper per item?

If those two angles = 180, then lines u and v are parallel.

90 + (x+102) = 180

192 + x = 180

x = 180-192

x = -12

So if x = -12, then lines u and v are parallel.

Answer:

x = -12

Step-by-step explanation:

90 + x + 102 = 180

192 + x = 180

x = -12

Therefore, in order for lines u and v to be parallel, the value of x must be -12

Since we don't have the initial population size N(0), we'll represent it as a variable. The logistic equation for this population will be: N(t) = 2506 / (1 + (2506 - N0) / (N0 * e^(-0.018 * t))). This equation describes the population growth over time based on the given r value and carrying capacity.

The logistic model is used to describe population growth that is limited by a carrying capacity. In this case, the carrying capacity is given as 2506. The value of r, which represents the maximum growth rate of the population, is given as 0.018.
The logistic equation is given by:
dN/dt = rN(1-N/K)
where N is the population size, t is time, r is the intrinsic growth rate, and K is the carrying capacity.
Given that the carrying capacity is 2506 and the initial population size is n(0), we can rewrite the equation as:
dN/dt = 0.018N(1-N/2506)
This equation describes how the population size changes over time based on the initial population size and the carrying capacity. The equation predicts that as the population approaches the carrying capacity, the growth rate slows down until it eventually levels off.
In summary, the logistic equation satisfied by the population with an initial size of n(0) is dN/dt = 0.018N(1-N/2506), and it can be used to predict how the population size changes over time. This equation shows that population growth is not always unlimited and can be influenced by environmental factors such as carrying capacity.
Based on the information provided, we can construct a logistic equation for the given population growth model. The logistic model is represented by the equation:
N(t) = K / (1 + (K - N0) / (N0 * e^(-r * t)))
Where:
- N(t) is the population size at time t
- K is the environmental carrying capacity (in this case, 2506)
- N0 is the initial population size (N(0))
- r is the intrinsic growth rate (0.018)
- e is the base of the natural logarithm (approximately 2.718)
- t is the time
Since we don't have the initial population size N(0), we'll represent it as a variable. The logistic equation for this population will be:
N(t) = 2506 / (1 + (2506 - N0) / (N0 * e^(-0.018 * t)))
This equation describes the population growth over time based on the given r value and carrying capacity.

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The expected value of the number of points you get is 0.

To find the expected value of the number of points you get, we need to calculate the probability of getting each outcome (rolling a prime number or rolling a composite number) and multiply it by the corresponding points.

Here's how we can do that:

There are 10 possible outcomes when rolling the ten-sided die, each with an equal probability of 1/10.

Prime numbers on the die: 2, 3, 5, 7 (total 4 numbers)

Composite numbers on the die: 4, 6, 8, 9 (total 4 numbers)

For prime numbers (4 possible outcomes):

Probability of rolling a prime number = Number of prime numbers / Total possible outcomes = 4/10 = 2/5

Points gained for rolling a prime number = 1

For composite numbers (4 possible outcomes):

Probability of rolling a composite number = Number of composite numbers / Total possible outcomes = 4/10 = 2/5

Points lost for rolling a composite number = -1

Expected value = (Probability of prime number [tex]\times[/tex]Points gained) + (Probability of composite number [tex]\times[/tex] Points lost)

Expected value = (2/5 [tex]\times[/tex] 1) + (2/5 [tex]\times[/tex]   -1)

Expected value = 2/5 - 2/5

Expected value = 0

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Answer:

Step-by-step explanation:

You want the measures of the angles marked x° and y° in the given diagram.

The measure of an inscribed angle is half the measure of the arc it intercepts. This means any inscribed angles that intercept the same arc will have the same measure.

The inscribed angles with vertices J and K both intercept arc FH, so both have the marked measure of 56°.

  x = 56

The angle where the chords cross (y°) will be half the sum of the arcs those chords intercept. Here, those are arcs FH and JK.

Given that half the arc measure is the measure of the intercepting inscribed angle, we can simply sum the inscribed angles to get y°:

  y° = 56° +19° = 75°

  y = 75

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The average rate of change of the function over the interval 3 ≤ x ≤ 7 is 3/2 or 1.5.

To find the average rate of change of a function over an interval, we can use the formula:

average rate of change = (f(b) - f(a)) / (b - a)

where a and

b are the endpoints of the interval and f(x) is the function.

Using the values from the table, we have:

a = 3, b = 7

f(a) = 2, f(b) = 8

Therefore, the average rate of change of the function over the interval 3 ≤ x ≤ 7 is:

average rate of change = (f(b) - f(a)) / (b - a) = (8 - 2) / (7 - 3) = 6/4 = 3/2

So the average rate of change of the function over the interval 3 ≤ x ≤ 7 is 3/2 or 1.5.

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Step-by-step explanation:

if you gave us the whole information, then we have 4 cards with the values : 4, 5, 6 and 7.

the probabilty to pick the card with the value 4 is the same as the probabilty to pick a card with value less than 5.

in both cases there is only one card for the desired outcome : 4.

therefore, P(4 or less than 5) = P(4)

a probability is always the ratio

desired cases / totally possible cases

so, in our case the probabilty to pick one specific card out of a total of 4 cards is

1/4

and so, the probability to pick 4 is

P(4) = 1/4.

Answer:

0.18 litres

Step-by-step explanation:

To find out how much blackcurrant juice Ellie should add, we first need to determine how much space is left in the litre after she adds the apple and orange juice.

We can start by adding the apple and orange juice:

0.32 L + 0.5 L = 0.82 L

This means that there is 1 L - 0.82 L = 0.18 L of space left in the litre for the blackcurrant juice.

Therefore, Ellie should add 0.18 litres of blackcurrant juice to make 1 litre of her fruit cocktail.

Answer:

(5/2, 3/2)

Step-by-step explanation:

A = (1, 4)

B = (4, -1)

((x1 + x2)/2, (y1 + y2)/2) = midpoint formula

(x1, y1) = (1, 4) and (x2, y2) = (4, -1)

((1 + 4)/2, (4 + (-1))/2) =

5/2 , 3/2

The final answer is So, to compute the probability, we need to find P(Z > 0.2) and subtract it from 1.

The random variable of interest in this scenario is the total time taken to download all 90 files and complete the installation of the software package.

This random variable is continuous since it represents a time duration, which can take on any value within a range. To compute the probability that the installation takes more than 28 minutes, we first need to calculate the mean and standard deviation of the total download time.

The mean download time for one file is given as 18 seconds, so the mean download time for 90 files is (18 seconds/file) * 90 files = 1620 seconds.

The standard deviation of the download time for one file is 10 seconds. Since the files are downloaded independently, the standard deviation of the total download time for 90 files can be calculated using the formula for the standard deviation of the sum of independent random variables:

Standard deviation of the total download time = square root(90) * 10 seconds =[tex]30 * 10[/tex] seconds = 300 seconds.

Now, to find the probability that the installation takes more than 28 minutes (which is equivalent to 28 minutes * 60 seconds = 1680 seconds), we need to standardize the value using the z-score formula:[tex]z = (x - μ) /[/tex]∅

where x is the desired time (1680 seconds), μ is the mean download time (1620 seconds), and σ is the standard deviation (300 seconds).

z = [tex]\frac{(1680 - 1620) }{300}[/tex]= [tex]\frac{60}{300}[/tex][tex]= 0.2[/tex]

Using a standard normal distribution table or a calculator, we can find the probability associated with a z-score of 0.2. The probability that the installation takes more than 28 minutes is equal to 1 minus this probability, as we are interested in the probability of the installation taking more time.

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Therefore, there are 16,807,680 different combinations of pizzas that can be made if each pizza can have any number of toppings, including no toppings, but no two pizzas can have the same set of toppings and the same topping cannot be used more than once.

There are 2^5 = 32 possible combinations of toppings for a single pizza, since each topping can either be included or not. However, since no two pizzas can have the same set of toppings, once a combination is used for one pizza, it cannot be used again.

Therefore, for the first pizza, there are 32 possible combinations of toppings. For the second pizza, there are only 31 possible combinations left, since the combination used for the first pizza cannot be used again. For the third pizza, there are 30 possible combinations left, and so on.

So the total number of different combinations of pizzas that can be made is:

32 x 31 x 30 x 29 x 28 = 16,807,680

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The probability that a randomly chosen table orders at least one appetizer is 0.40, which corresponds to option b. 0.40.

The probability that a randomly chosen table orders at least one appetizer can be calculated by adding the probabilities of the table ordering 1, 2, or 3 or more appetizers. Therefore, the probability is:

0.35 + 0.04 + 0.01 = 0.40

Therefore, the correct answer is b. 0.40. It is important to note that this probability distribution can be used to make informed decisions about how much of each appetizer to stock and how to price them to maximize profits. The management of the chain of restaurants can also use this information to predict the demand for appetizers and adjust their marketing strategy accordingly. Additionally, they can use this information to monitor their performance and identify areas of improvement in their service or menu.

To find the probability that a randomly chosen table orders at least one appetizer, we need to consider the probabilities of ordering 1, 2, or 3 or more appetizers. In this case, the probability distribution is given as:

Value of X:       0     1     2     3 or more
Probability:    0.60  0.35  0.04  0.01

To calculate the probability of a table ordering at least one appetizer, we need to add the probabilities for 1, 2, and 3 or more appetizers:

P(at least one appetizer) = P(1) + P(2) + P(3 or more)
P(at least one appetizer) = 0.35 + 0.04 + 0.01

Now, we sum the probabilities:

P(at least one appetizer) = 0.35 + 0.04 + 0.01 = 0.40

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It's not entirely clear what is meant by "5 Apples in 6 rows," so I will provide a general answer that could apply to a few different interpretations of the question.

If Johnny has 5 apples and places them in 6 rows, the answer to how many apples he will have left depends on how many apples are in each row and what Johnny does with them. For example, if he eats one apple from each row, he will be left with 5 - 6 = -1 apples, which doesn't make sense. If instead he rearranges the apples into one row, he will still have 5 apples. If he gives away 2 apples, he will have 3 apples left.

In summary, the number of apples Johnny will have left depends on the details of the scenario, including how many apples are in each row and what Johnny does with them.

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Based on the negative correlation of -0.74, we can expect that if a smoker who had never been to church started attending church regularly, they would smoke less cigarettes.

However, it is important to note that correlation does not necessarily imply causation, and there may be other factors that could also influence the smoker's cigarette consumption. Therefore, while this correlation provides insight into the relationship between church attendance and smoking habits, it is not a definitive predictor of individual behavior.

Based on the correlation of -0.74, we can expect that as the number of church visits increases, the number of cigarettes smoked will likely decrease. Therefore, if a smoker who had never been to church starts attending regularly, we should expect that the smoker will smoke less cigarettes. Keep in mind that correlation does not imply causation, so this is not a guaranteed outcome, but it suggests a possible trend based on the data collected.

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The confidence interval for the population mean of approximately (2.973, 3.427)

The maximum error

ME = 1.96 * (1.8 / √240)

ME ≈ 1.96 * (1.8 / 15.49)

ME  1.96 * 0.116

= 0.227

So, the maximum error of the estimate for this 95% confidence interval is approximately 0.227.

Since we are given the sample mean (x) = 3.2, we can use that to estimate the population mean (μ):

μ =x ± ME

μ = 3.2 ± 0.227

3.2 - 0.227 , 3.2 + 0.227

This gives us a 95% confidence interval for the population mean of approximately (2.973, 3.427).

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To find the dimensions of the largest room that can be built with a fixed perimeter of 600 feet.

We need to divide the perimeter by 2 and use that as the sum of two adjacent sides. Let's call the length of the rectangle "l" and the width "w".
So we have:  2l + 2w = 600
Simplifying:  l + w = 300
We want to maximize the area of the rectangle, which is given by:  A = lw
We can solve for one variable in terms of the other:  l = 300 - w
Substituting into the area equation:
A = (300 - w)w
A = 300w - w^2
To maximize the area, we need to find the value of w that makes the derivative of A with respect to w equal to 0:  dA/dw = 300 - 2w = 0
w = 150
So the width of the rectangle is 150 feet. Substituting back into the perimeter equation: l + 150 = 300
l = 150
So the length of the rectangle is also 150 feet.
Therefore, the largest room that can be built has dimensions 150 ft by 150 ft, and its area is:  A = lw = 150 * 150 = 22,500 ft^2
The dimensions of the largest rectangular room a carpenter can build with a fixed perimeter of 600 feet are 150 ft by 150 ft. The area of this room is 22,500 ft². This is because when the length and width are equal, the area of the rectangle is maximized.

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we can answer it as follow

The red one show the GCF factor form it is -7 then you you ommit negative of numinator by negative of denominator . then you multiply both side by 4/7

the you simplify and solve a .

Answer: Jina bought 5 pounds of coffee by spending a total of $38.60.

Step-by-step explanation:

According to this problem, Jina has an $80 gift card for a coffee store and when she bought some pounds of coffee, she had $41.40 left.

To solve this equation you will need to rephrase this equation to

80 - 41.40 = x

When you subtract the problem, you should get $38.60.

80 - 41.40 = 38.60

Now since Jina bough coffee that costs $7.72 per pound, you will need to divide that by the amount you have just subtracted.

38.60 ÷ 7.72

When you divide "38.60 ÷ 7.72", you should get the number 5.

Therefore, Jina bought 5 pounds worth of coffee, making her total on her gift card $38.60. Hope this helps!

-From 5th Grade Honors Student

Answer:

x ≈ 50.7

Step-by-step explanation:

x/sin 90  =  23/sin(180-90-63) = 23/sin 27

x = (23 X sin 90) / sin 27

  ≈ 50.7

Answer:

x^3+5x^2+11x+10

Step-by-step explanation:

Multiply each term in the first expression by each term in the second expression and combine like terms.

have a great day and thx for your inquiry :)

By downloading the data, Madison will have access to the necessary information to analyze. Reformatting the dates to be in the same time zone will allow for easier analysis and comparison of the data.

The following steps should be ordered as follows for Madison to project precipitation for the following year:

1. Download the precipitation data from the USGS website
2. Reformat the dates on all precipitation data to be in the same time zone
3. Cluster the data into different seasons and states and perform a regression to predict precipitation in each cluster
4. Create a line chart that shows precipitation by state and by season

Clustering the data into different seasons and states and performing a regression analysis will allow for predictions of precipitation in each cluster. Finally, creating a line chart will provide a visual representation of the data, allowing for easier interpretation and analysis.

To help Madison study the precipitation data and make projections, she should follow these steps in order:

1. Download the precipitation data from the USGS website.
2. Reformat the dates on all precipitation data to be in the same time zone.
3. Cluster the data into different seasons and states and perform a regression to predict precipitation in each cluster.
4. Create a line chart that shows precipitation by state and by season.

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To evaluate the given integral, we need to plug in the limits of integration, which are 0 and 4, into the antiderivative of the integrand.

The antiderivative of 4/5 t^3 - 3/4 t^2 + 2/5 t is:

(4/5) * (t^4/4) - (3/4) * (t^3/3) + (2/5) * (t^2/2) + C

where C is the constant of integration.

Now, plugging in the limits of integration:

[(4/5) * (4^4/4) - (3/4) * (4^3/3) + (2/5) * (4^2/2)] - [(4/5) * (0^4/4) - (3/4) * (0^3/3) + (2/5) * (0^2/2)]

Simplifying this expression, we get:

(256/5 - 64 + 16/5) - (0 - 0 + 0)

= 240/5

= 48

Therefore, the value of the given integral is 48.

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To evaluate the integral ∫[0, 4] (4/5t^3 - 3/4t^2 + 2/5t) dt, we can use the power rule of integration.

Applying the power rule, we can integrate each term of the polynomial separately:

∫ (4/5t^3) dt = (4/5) * (1/4) * t^4 + C1 = t^4/5 + C1

∫ (-3/4t^2) dt = (-3/4) * (1/3) * t^3 + C2 = -t^3/4 + C2

∫ (2/5t) dt = (2/5) * (1/2) * t^2 + C3 = t^2/5 + C3

Adding the constants of integration, we can write the complete integral:

∫[0, 4] (4/5t^3 - 3/4t^2 + 2/5t) dt = (t^4/5 + C1) - (t^3/4 + C2) + (t^2/5 + C3)

To evaluate the definite integral between the limits 0 and 4, we substitute the upper limit (4) and lower limit (0) into the expression:

[(4^4/5 + C1) - (4^3/4 + C2) + (4^2/5 + C3)] - [(0^4/5 + C1) - (0^3/4 + C2) + (0^2/5 + C3)]

Simplifying the expression further, we get:

[(1024/5 + C1) - (0 + C2) + (16/5 + C3)] - [(0 + C1) - (0 + C2) + (0 + C3)]

Since the constants of integration cancel out, we are left with:

[(1024/5) - (0) + (16/5)] - [(0) - (0) + (0)]

= 1024/5 + 16/5

= 1040/5

= 208

Therefore, the value of the integral ∫[0, 4] (4/5t^3 - 3/4t^2 + 2/5t) dt is 208.

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C, figure C

hope this helps, and have a good day! :)

Answer:

We have parallel lines intersected by a transversal.

Corresponding angles are congruent:

5q + 3 = 3q + 11

2q = 8, so q = 4

Alternate interior angles are congruent:

3r - 4 = 6r - 19

3r = 15, so r = 5

Consecutive interior angles are supplementary:

4s + s + 90 = 180

5s = 90, so s = 18

Supplementary angles:

2t + 20 = 4t + 10

2t = 10, so t = 5

Answer:

(1/2)(15)(7 + 15) = (1/2)(22)(15) = 165 m^2

Answer:

165m²

Step-by-step explanation:

First you make it into a triangle and rectangle.  The rectangle would be 15x7.  The triangle would be 1/2x15x8.

15x7=105

1/2x15x8=60

105+60=165 meters squared

In triangle ABC, the length of AC is 13 units

In triangle DEF, the length of DE is 24 units

By pythagoras theorem we find the missing length

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

In triangle ABC, we have to find length of AC

AC² = 5² + 12²

=25+144

=169

AC=13 units

In triangle DEF, we have to find length of DE

DF² =DE² + EF²

26²=DE² + 10²

676=DE² + 100

576=DE²

DE=24 units

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The ratio of the length of a piece of metal pipe to the length of a piece of plastic tubing is,

⇒ 1 : 8

We have to given that;

He used 1/3 yard of metal pipe divided into 4 equal pieces, and 2 yards of plastic tubing divided into 3 equal pieces.

Hence, Length of piece of metal pipe = 1/4×3 = 1/12

And, length of a piece of plastic tubing is, 2 / 3

So, The ratio of the length of a piece of metal pipe to the length of a piece of plastic tubing is,

⇒ (1/12) : (2/3)

⇒ (1/12) x (3/2)

⇒ 1/8

⇒ 1 : 8

Thus, The ratio of the length of a piece of metal pipe to the length of a piece of plastic tubing is,

⇒ 1 : 8

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Answer:

Step-by-step explanation:

The given set of points is:

{(3,4),(-2,3),(7,1),(-2,0.5),(-0.5,4)}

To determine if this set of points represents a function or not, we need to check if each input (x-coordinate) has a unique output (y-coordinate). We also need to find the domain and range of the set of points.

Domain:

The domain of a function is the set of all possible input values (x-coordinates) for which the function is defined. In this case, the domain is simply the set of all x-coordinates of the given points. Therefore, the domain is:

{-2, -0.5, 3, 7}

Range:

The range of a function is the set of all possible output values (y-coordinates) that the function can produce. In this case, the range is simply the set of all y-coordinates of the given points. Therefore, the range is:

{0.5, 1, 3, 4}

Functionality:

To determine if the given set of points represents a function, we need to check if each x-coordinate has a unique y-coordinate. We can see that all x-coordinates in the domain have a unique y-coordinate in the range. Therefore, the given set of points represents a function.

In summary:

Domain: {-2, -0.5, 3, 7}

Range: {0.5, 1, 3, 4}

Functionality: The given set of points represents a function.

The circumference of the football field is given as 264 meters.

Let's assume that the radius of the football field is "r" meters. We know that the circumference of a circle is given by the formula C=2πr, where C is the circumference and r is the radius.

Therefore, we have:

C = 2πr

264 = 2πr   (since C = 264 meters)

132 = πr

Now we can solve for the radius:

r = 132/π ≈ 42

Therefore, the radius of the football field is approximately 42 meters, rounded to the nearest whole number.

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Answer:

The slope of this line is 1/4.

The correct answer is D.

Answer:

$16.48

Step-by-step explanation:

If 6% is sales tax, that means that the total cost of the doll is 106% of the original cost. (basically 100% is the originall doll, and you add 6% of the tax). If you convert 106% from percentage form to decimal form (which you do by dividing by 100), 106% is the same as 1.06 times the original cost of the doll.

Thus you do 1.06 x 15.55 = 16.483 which rounds down to $16.48