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SashulF [63]
1 year ago
5

A newly drilled water well produces 50,000 quarts of water per week. With no new water feeding the well, the production drops by

5% per year. Using 52 weeks in a year, what is the total number of quarts of water that can be drawn from this water well before it goes dry?
Mathematics
1 answer:
Sveta_85 [38]1 year ago
5 0

Answer:

Total amount of water = 5,200,000

Step-by-step explanation:

Given:

water produced = 50,000 quarts of water per week

Production drop = 5% = 0.05 per year

Number of week in year = 52 week

Find:

Total amount of water

Computation:

Sum = a / r

a = 50,000 x 52

a = 2,600,000

Sum = a / [1-r]

Sum = 2,600,000 / 5%

Sum = 2,600,000 / 0.05

Total amount of water = 5,200,000

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choli [55]

Answer:

48 cm

Step-by-step explanation:

Given:

Distance of rod from the wall = 45 cm

Distance of rod from the light = 15 cm

Length of rod = 12 cm

We can see that <DAM and <BAF are equal

Also, <DMA and <BFM are equal because they are corresponding angles

To find the length of the shadow, let's take the equation

\frac{DM}{BF} = \frac{AM}{A.F}

Where.:

DM = ½ of length of the rod = ½*12 = 6

A.F = 15 + 45 = 60 cm

AM = 15 cm

Therefore,

\frac{DM}{BF} = \frac{AM}{A.F}

= \frac{6}{BF} = \frac{15}{60}

Cross multiplying, we have:

15 * B.F = 60 * 6

15 * B.F = 360

BF = \frac{360}{15}

BF = 24 cm

The shadow on the wall =

2 * BF

= 2 * 24

= 48 cm

The shadow on the wall is 48 cm

7 0
1 year ago
What type of triangle has side lengths of 4√5, √145 and 19?
Masja [62]

a, b, c - side lengths (a ≤ b ≤ c)

If a^2+b^2 < c^2, then is Obtuse triangle.

If a^2+b^2=c^2, then is Right triangle.

If a^2+b^2 > c^2, then Acute triangle.

a=4\sqrt5,\ b=\sqrt{145},\ c=19\to a < b < c

Check to see if the sum of the first two sides is greater than the third.

a+b=4\sqrt5+\sqrt{145}\approx9+12=21 > 19=c\\\\CORRECT

a\neq b\neq c\neq a, therefore is Scalene triangle.

a^2=(4\sqrt5)^2=4^2(\sqrt5)^2=16(5)=80\\\\b^2=(\sqrt{145})^2=145\\\\c^2=19^2=361\\\\a^2+b^2=80+145=225 < 361=c^2\\\\a^2+b^2 < c^2

It's Obtuse triangle.

5 0
2 years ago
Scott likes to run long distances. He can run 20 \text{ km}20 km20, start text, space, k, m, end text in 858585 minutes. He want
aleksandrvk [35]

Answer:

<em>Scott will take 221 minutes to run 52 km</em>

Step-by-step explanation:

<u>Speed</u>

The speed of an object can be calculated with the formula:

\displaystyle v=\frac{d}{t}

Where d is the distance traveled and t is the time taken.

Scott can run d=20 km in 85 minutes. Thus, his speed is:

\displaystyle v=\frac{20}{85}\ km/min

Now he wants to know how many minutes it will take him to run d=52 km. Solving the formula for t:

\displaystyle t=\frac{d}{v}

Since the speed has been already determined:

\displaystyle t=\frac{52}{\frac{20}{85}}

Multiplying by the reciprocal of the denominator:

\displaystyle t=52*\frac{85}{20}

t = 221 min

Scott will take 221 minutes to run 52 km

4 0
2 years ago
Read 2 more answers
Scores on Ms. Bond's test have a mean of 70 and a standard deviation of 11. David has a score of 52 on Ms. Bond's test. Scores o
otez555 [7]

Answer:

Due to the higher z-score, David has the higher standardized score

Step-by-step explanation:

Z-score:

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Which student has the higher standardized score

Whoever had the higher z-score.

David:

Scores on Ms. Bond's test have a mean of 70 and a standard deviation of 11. David has a score of 52 on Ms. Bond's test. So X = 52, \mu = 70, \sigma = 11

Z = \frac{X - \mu}{\sigma}

Z = \frac{52 - 70}{11}

Z = -1.64

Steven:

Scores on Ms. Nash's test have a mean of 64 and a standard deviation of 6. Steven has a score of 52 on Ms. So X = 52, \mu = 64, \sigma = 6

Z = \frac{X - \mu}{\sigma}

Z = \frac{52 - 64}{6}

Z = -2

Due to the higher z-score, David has the higher standardized score

3 0
2 years ago
The graphs shown are of the form y = ax2. Which graph has the smallest value for a?
Talja [164]
y= x^{2} is a parabola (looks like the letter U).

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The absolute value of a (the number without the sign) controls how wide or narrow it is. If the absolute value is a fraction less than 1 the graph gets wider. The smaller the absolute value of the fraction the wider the graph gets.

If the absolute value of a is greater than 1 the graph gets narrower (it gets skinnier). The bigger the absolute value the narrower the graph.

So, if all the graphs look like a U (concave up) then the one with the smallest a is the one that is the widest.

The a also controls whether the graph is concave up or concave down. If a is negative

If a is negative the graph is concave down so any graph that is concave down has a smaller value of a than any graph that is concave up. However, if the graph is concave down the one with the smallest a would be the most narrow one.

So to find the one with the smallest a...
If they are all concave up (like a U) pick the widest one
and
If they are not all concave up pick the narrowest one that is concave down (looks like an upside down U)
3 0
2 years ago
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