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1 year ago

The price of a ring was increased by 30% to £325. What was the price before the increase?

Mathematics

2 answers:

Oxana [17]1 year ago

7 0

Answer:

The cost before the increase is £250.

Step-by-step explanation:

Given that after 30% increases, the cost of the ring is £325 so we can assume that 130% is £325. Now, we have to form an expression in term of x where x represents the original cost :

$\frac{130}{100} \times x = 325$

Next, we have to solve it :

$x = 325 \div \frac{130}{100}$

$x = 325 \times \frac{100}{130}$

$x = 250$

Radda [10]1 year ago

3 0

Answer:

227.5

Step-by-step explanation:

Find the number that is increased by 30% to get to 325.

100-30 = 70.

In other words, what number is 70% of 325.

325 x .70 = 227.5

The original price of the ring was 227.5.

Check your work, 227.5 = 70% of X

227.5 / .70 = 325

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1 year ago

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Line AB has an equation of a line y = 5x − 2. Which of the following could be an equation for a line that is parallel to line AB

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Determine the slope of line AB
m = 5

Determine the slope of the lines from the options
First option: y = 5x + 3, the slope is 5
Second option: y = (1/5)x + 3, the slope is 1/5
Third option: y = -5x + 3, the slope is -5
Fourth option: y = (-1/5)x + 3, the slope is -1/5

Parallel lines are similar in the slope. So the line which is parallel to line AB must have the slope of 5.

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2 years ago

Suppose that only 20% of all drivers come to a complete stop at an intersection having flashing red lights in all directions whe

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Answer:

a) 91.33% probability that at most 6 will come to a complete stop

b) 10.91% probability that exactly 6 will come to a complete stop.

c) 19.58% probability that at least 6 will come to a complete stop

d) 4 of the next 20 drivers do you expect to come to a complete stop

Step-by-step explanation:

For each driver, there are only two possible outcomes. Either they will come to a complete stop, or they will not. The probability of a driver coming to a complete stop is independent of other drivers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

20% of all drivers come to a complete stop at an intersection having flashing red lights in all directions when no other cars are visible.

This means that $p = 0.2$

20 drivers

This means that $n = 20$

a. at most 6 will come to a complete stop?

$P(X \leq 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{20,0}.(0.2)^{0}.(0.8)^{20} = 0.0115$

$P(X = 1) = C_{20,1}.(0.2)^{1}.(0.8)^{19} = 0.0576$

$P(X = 2) = C_{20,2}.(0.2)^{2}.(0.8)^{18} = 0.1369$

$P(X = 3) = C_{20,3}.(0.2)^{3}.(0.8)^{17} = 0.2054$

$P(X = 4) = C_{20,4}.(0.2)^{4}.(0.8)^{16} = 0.2182$

$P(X = 5) = C_{20,5}.(0.2)^{5}.(0.8)^{15} = 0.1746$

$P(X = 6) = C_{20,6}.(0.2)^{6}.(0.8)^{14} = 0.1091$

$P(X \leq 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.0115 + 0.0576 + 0.1369 + 0.2054 + 0.2182 + 0.1746 + 0.1091 = 0.9133$

91.33% probability that at most 6 will come to a complete stop

b. Exactly 6 will come to a complete stop?

$P(X = 6) = C_{20,6}.(0.2)^{6}.(0.8)^{14} = 0.1091$

10.91% probability that exactly 6 will come to a complete stop.

c. At least 6 will come to a complete stop?

Either less than 6 will come to a complete stop, or at least 6 will. The sum of the probabilities of these events is decimal 1. So

$P(X < 6) + P(X \geq 6) = 1$

We want $P(X \geq 6)$ . So

$P(X \geq 6) = 1 - P(X < 6)$

In which

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0115 + 0.0576 + 0.1369 + 0.2054 + 0.2182 + 0.1746 = 0.8042$

$P(X \geq 6) = 1 - P(X < 6) = 1 - 0.8042 = 0.1958$

19.58% probability that at least 6 will come to a complete stop

d. How many of the next 20 drivers do you expect to come to a complete stop?

The expected value of the binomial distribution is

$E(X) = np = 20*0.2 = 4$

4 of the next 20 drivers do you expect to come to a complete stop

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2 years ago

Kate recorded what she ate for breakfast every day for six months. Her findings are shown in the graph below. A bar graph titled

Amiraneli [1.4K]

Answer: The correct answer is option B: 19%

Step-by-step explanation: The bar graph according to the question has the following set of data;

Cereal ----------34

Eggs and Bacon ----------21

Pastries ----------39

Bagels ----------48

Waffles ----------38

The total from this set of data is 180 (that is the summation of all the observed data). The portion taken up by cereals can be derived as follows;

Cereal = (34/180) x 360

Cereal = 68 degrees

Note that we have used degrees as the unit since the data would be transferred to a pie chart. Hence on the pie chart it occupies 68 degrees of the entire 360 degrees.

In order to find out what percentage this represents we can now express 68 degrees as a percentage as follows;

Cereal = (68/360) x 100

Cereal = 18.8888888

Cereal ≈ 19

Therefore cereal occupies 19 percent of the pie chart.

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1 year ago

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