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3 years ago

Donna is putting money into a savings account. She starts with $450 in the savings account, and each week she adds $70.

Mathematics

1 answer:

kvv77 [185]3 years ago

7 0

Answer:

1430

Step-by-step explanation:

S=450+70T

S= 450 + 70(14)

S=450+980

S=1430

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The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20 per cent.Find the single reduction the

Evgen [1.6K]

Answer:

40% . The single reduction together is 40%.

Step-by-step explanation:

Let the bicycle cost is x before reduced price.

First 25% is reduced and again 20% further reduced.

Let the single reduction is y% if the two reduction together are equal.

Solution,

Case .1

reduction cost $=x\times 25%$ %

$=x\times 25/100$

$=x/4$

The cost of bicycle after reduction of 25% is

$=x-x/4=3x/4$

cost of reduction further reduction of 20% $=3x/4\times 20$ %

$=3x\times 20/(4\times 100)$

$=3x/20$

The new cost of bicycle is further reduction of 20% is

$=3x/4-3x/20$

$=\left ( 15x-3x \right )/20$

$=12x/20=3x/5$

Case.2

if single reduction is done new cost of cycle is equal

$x-x\times y$ %= $3x/5$

$x\left ( 1-y/100 \right )=3x/5$

$\left ( 100-y \right )/100=3/5$

$100-y=60$

$y=40$ %

single reduction of a cycle is 40%

8 0

3 years ago

Question 12 (1 point) Given P(A) 0.34, P(A and B) 0.27, P(A or B) 0.44, what is P(B)? Answer in decimal form. Round to 2 decimal

Tema [17]

Answer: The required probability of event B is P(B) = 0.37.

Step-by-step explanation: For two events A and B, we are given the following probabilities :

P(A) = 0.34, P(A ∩ B) = 0.27 and P(A ∪ B) = 0.44.

We are to find the probability of event B, P(B) = ?

From the laws of probability, we have

$P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\\Rightarrow 0.44=0.34+P(B)-0.27\\\\\Rightarrow 0.44=0.07+P(B)\\\\\Rightarrow P(B)=0.44-0.07\\\\\Rightarrow P(B)=0.37.$

Thus, the required probability of event B is P(B) = 0.37.

6 0

3 years ago

Please help i've been stuck on these for a bit now!

lisov135 [29]

Answer:

Q6. D

Q8. A

Step-by-step explanation:

Q6. In 40 trials, he flipped '2 heads and 1 tail' 16 times.

For 2 heads, probability= 16/40= 4/10

For 120 trials, number of times= 4/10 × 120= 48

Q8.

$125x + 200 \geqslant 1200 \\ 125x \geqslant 1200 - 200 \\ 125x \geqslant 1000 \\ x \geqslant 1000 \div 125 \\ x \geqslant 8$

Answer is A because the inequality shows that x is equal or greater than 8 so the dot at 8 has to be coloured.

Note that we do not change the inequality sign unless we are dividing the whole thing by -1.

5 0

3 years ago

Rewrite as a power of 10: 1/10

Yuliya22 [10]

Answer:

Step-by-step explanation:

You have to know how negative exponents "work" to understand this concept.

$\frac{1}{10}=10^{-1$ because if you want to make a negative exponent positive you put what the exponent is on under a 1. It follows then that you can go backwards from that and rewrite positive fractions with negative exponents.

4 0

3 years ago

With a height of 68 in, Nelson was the shortest president of a particular club in the past century. The club presidents of the

Ivahew [28]

Answer:

a. The positive difference between Nelson's height and the population mean is: $\\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in$ .

b. The difference found in part (a) is 1.174 standard deviations from the mean (without taking into account if the height is above or below the mean).

c. Nelson's z-score: $\\ z = -1.1739 \approx -1.174$ (Nelson's height is below the population's mean 1.174 standard deviations units).

d. Nelson's height is usual since $\\ -2 < -1.174 < 2$ .

Step-by-step explanation:

The key concept to answer this question is the z-score. A z-score "tells us" the distance from the population's mean of a raw score in standard deviation units. A positive value for a z-score indicates that the raw score is above the population mean, whereas a negative value tells us that the raw score is below the population mean. The formula to obtain this z-score is as follows:

$\\ z = \frac{x - \mu}{\sigma}$ [1]

Where

$\\ z$ is the z-score.

$\\ \mu$ is the population mean.

$\\ \sigma$ is the population standard deviation.

From the question, we have that:

Nelson's height is 68 in. In this case, the raw score is 68 in $\\ x = 68$ in.
$\\ \mu = 70.7$ in.
$\\ \sigma = 2.3$ in.

With all this information, we are ready to answer the next questions:

a. What is the positive difference between Nelson's height and the mean?

The positive difference between Nelson's height and the population mean is (taking the absolute value for this difference):

$\\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in$ .

That is, the positive difference is 2.7 in.

b. How many standard deviations is that [the difference found in part (a)]?

To find how many standard deviations is that, we need to divide that difference by the population standard deviation. That is:

$\\ \frac{2.7\;in}{2.3\;in} \approx 1.1739 \approx 1.174$

In words, the difference found in part (a) is 1.174 standard deviations from the mean. Notice that we are not taking into account here if the raw score, x, is below or above the mean.

c. Convert Nelson's height to a z score.

Using formula [1], we have

$\\ z = \frac{x - \mu}{\sigma}$

$\\ z = \frac{68\;in - 70.7\;in}{2.3\;in}$

$\\ z = \frac{-2.7\;in}{2.3\;in}$

$\\ z = -1.1739 \approx -1.174$

This z-score "tells us" that Nelson's height is 1.174 standard deviations below the population mean (notice the negative symbol in the above result), i.e., Nelson's height is below the mean for heights in the club presidents of the past century 1.174 standard deviations units.

d. If we consider "usual" heights to be those that convert to z scores between minus2 and 2, is Nelson's height usual or unusual?

Carefully looking at Nelson's height, we notice that it is between those z-scores, because:

$\\ -2 < z_{Nelson} < 2$

$\\ -2 < -1.174 < 2$

Then, Nelson's height is usual according to that statement.

7 0

3 years ago