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Elena L [17]
2 years ago
8

Sophia and Scott each open a bank account with an initial deposit of $50 each. Scott planned to save 30% of his earnings from hi

s after-school job. The job pays $8 per hour, and he works 25 hours each week. For four weeks, Sophia saved $45 per week. After that, she saved an additional $30 per week. During which WEEK will they have the same amount of money in their bank accounts?
Mathematics
1 answer:
scoray [572]2 years ago
6 0

Answer:

During the 9th week

Step-by-step explanation:

Scott: 50 + (0.3)(8×25)t

= 50 + 60t

Sophia: 50 + 45t + 30(t-4)

= -70 + 75t

60t + 50 = 75t - 70

15t = 120

t = 8

After 8 weeks they will have the same amount,

Which is during the 9th week

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Monica has a bag of marbles. There are 4 red marbles and 7 blue marbles and 5 yellow marbles in a bag. Monica will randomly pick
natima [27]

Answer:

\frac{7}{64}\approx 0.11

Step-by-step explanation:

We have been given that there are 4 red marbles and 7 blue marbles and 5 yellow marbles in a bag. Monica will randomly pick two marbles out of the bag replacing the first marble before picking the second marble.

Since Monica will replace the first marble before picking the second marble, therefore, probability of both events will be independent and probability of occurring one event will not affect the probability of second event's occurring.          

Since the probability of two independent compound events is always the product of probabilities of both events.

P(\text{A and B})=P(A)*P(B)

Now let us find probability of picking a red marble out of 16 (4+7+5) marbles.

P(Red)=\frac{\text{Total red marbles}}{\text{Total marbles}}

P(Red)=\frac{4}{16}

Probability of picking blue ball out of 16 (4+7+5) marbles:

P(Blue)=\frac{\text{Total blue marbles}}{\text{Total marbles}}

P(Blue)=\frac{7}{16}

Now let us find probability of Monica picking a red and then a blue marble.

P(\text{Red and Blue})=\frac{4}{16}\times \frac{7}{16}

P(\text{Red and Blue})=\frac{1}{4}\times \frac{7}{16}

P(\text{Red and Blue})=\frac{7}{4*16}

P(\text{Red and Blue})=\frac{7}{64}

P(\text{Red and Blue})=0.109375\approx 0.11

Therefore, the probability of picking a red and then blue marble is \frac{7}{64}\approx 0.11.  

7 0
2 years ago
A civil engineer tested concrete samples to investigate the difference in strength, in newtons per square millimeter (N/mm2), be
xxTIMURxx [149]

Answer: d)In repeated samples of the same size, approximately 95 percent of the intervals constructed from the samples will capture the population difference in means.

Step-by-step explanation:

Confidence interval is constructed to estimate a range of values that could possibly contain the population parameter. This could be the population mean or population proportion. A 95 percent confidence interval does not mean 95% probability. It tells how confident that we are that the confidence interval contains the population proportion. If we construct 100 of the given confidence interval, we are confident that 95% of them would contain the true population parameter. Therefore, the correct option is

d)In repeated samples of the same size, approximately 95 percent of the intervals constructed from the samples will capture the population difference in means.

3 0
2 years ago
A sports car and a minivan run out of gas and are pushed to the side of the road. Which is easier to push, and why?
nirvana33 [79]

Answer:

The sports car, because it has less mass and therefore less inertia

Step-by-step explanation:

When an object has less inertia it is easier to be put into and out of motion, and a sports car would obviously weigh less than a van.

5 0
2 years ago
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What is the ratio of the afternoon to morning temperatures shown in the table? Temperatures Morning Afternoon 15 degrees. 30 deg
Nikitich [7]

Given:

Morning Temperature = 15 degrees, Afternoon Temperature = 30 degrees

Morning Temperature = 20 degrees, Afternoon Temperature = 40 degrees

Morning Temperature = 26 degrees, Afternoon Temperature = 52 degrees

To find:

The ratio of the afternoon to morning.

Solution:

Taking any one pair of morning and afternoon temperature, we can find the ratio.

Morning Temperature = 15 degrees

Afternoon Temperature = 30 degrees

\text{Ratio}=\dfrac{\text{Afternoon Temperature}}{\text{Morning Temperature}}

\text{Ratio}=\dfrac{30}{15}

\text{Ratio}=\dfrac{2}{1}

\text{Ratio}=2:1

Therefore, the correct option is C.

7 0
1 year ago
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Express 0.555... as a fraction in simplest form
cestrela7 [59]

Answer:

0.40404040.

Step-by-step explanation:

5 0
1 year ago
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