answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
wlad13 [49]
2 years ago
12

Shawna has $750 in the bank.she deposits $37.50 each week.Ruben has $850 in the bank.He deposits his paycheck of $102.75 every M

onday,and he spends about $70.25 each week.After how many weeks will they have the same amount of money in the bank?
Mathematics
1 answer:
erastova [34]2 years ago
8 0

Answer:

Step-by-step explanation:

Answer: it would take 20 weeks before the amount in both accounts would be the same.

Step-by-step explanation:

Let x represent the number of weeks that it will take either Ruben and Shawna to have the same amount of money in their account.

Let y represent the total amount that would be in Shawna's account after x weeks

Let z represent the total amount that would be in Ruben's account after x weeks

Shawna has $750 in the bank. She deposits $37.50 each week. This means that the total amount after x weeks would be

y = 37.5x + 750

Ruben has $850 in the bank. He deposits his paycheck of $102.75 every Monday,and he spends about $70.25 each week.. This means that the total amount after x weeks would be

z = 850 + 102.75x - 70.25x

z = 850 + 32.5x

To determine the number of weeks before the amount in both accounts will becomes the same, we would equate y to z. It becomes

37.5x + 750= 850 + 32.5x

37.5x - 32.5x = 850 - 750

5x = 100

x = 100/5 = 20

You might be interested in
One of the vertices of △PQR is P(2, −1). The midpoint of PQ is M(3, 0). The midpoint of QR is N(5, 3). Show that MN || PR and MN
VLD [36.1K]

Answer:

<em>See the proof below</em>

Step-by-step explanation:

Given the following coordinates

P(2, −1)

Midpoint of PQ M(3, 0)

We can get the coordinate point Q using the midpoint formula;

M(X,Y) = (x1+x2/2, y1+y2/2)

X = x1+x2/2

3 = 2+x2/2

6 = 2+x2

x2 = 6-2

x2 = 4

Y = y1+y2/2

0 = -1+y2/2

0 = -1 + y2

y2 = 0+1

y2 = 1

<em>Hence the coordinate of Q is (4, 1)</em>

Next is to get the coordinate of R

Given the midpoint of QR to be N(5, 3)

(5,3) = (4+x2/2, 1+y2/2)

5 = 4+x2/2

10 = 4+x2

x2 = 10-4

x2 = 6

1+y2/2 = 3

1+y2 = 6

y2 = 6-1

y2 = 5

<em>Hence the coordinate of R is (6,5)</em>

<em></em>

Given the coordinates M(3, 0) and N(5, 3)

Slope is expressed as:

m = y2-y1/x2-x1

m = 3-0/5-3

m = 3/2

Slope of MN = 3/2

Get the slope of PR

Given the coordinates P(2, −1) and R (6,5)

Slope of PR = 5-(-1)/6-2

Slope of PR = 5+1/4

Slope of PR = 6/4 = 3/2

<em>Since the slope of MN is equal to that of PR, hence MN is parallel to PR i.e MN || PR</em>

<em></em>

To show that MN = 1/2PR, we will have to take the distance between M and N and also P and R first as shown:

For MN with coordinates  M(3, 0) and N(5, 3)

MN = √(x2-x1)²+(y2-y1)²

MN = √(5-3)²+(3-0)²

MN = √2²+3²

MN = √13

Get the length of PR where P(2, −1) and R (6,5)

PR = √(6-2)²+(5+1)²

PR = √4²+6²

PR = √16+36

PR = √52

PR = √4*13

PR = √4*√13

PR = 2√13

Since MN = √13

PR = 2MN

Divide both sides by 2

PR/2 = 2MN/2

PR/2 = MN

Hence MN = 1/2 PR (Proved!)

8 0
1 year ago
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past
Volgvan

Answer: We reject the null hypothesis, and we use Normal distribution for the test.

Step-by-step explanation:

Since we have given that

We claim that

Null hypothesis : H_0:\mu\geq 50000

Alternate hypothesis : H_1:\mu

There  is 5% level of significance.

\bar{X}=46800\\\\\sigma=9800\\\\n=29

So, the test statistic would be

z=\dfrac{\bar{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\z=\dfrac{46800-50000}{\dfrac{9800}{\sqrt{29}}}\\\\z=-1.75

Since alternate hypothesis is left tailed test.

So, p-value = P(z≤-2.31)=0.0401

And the P-value =0.0401 is less than the given level of significance i.e. 5% 0.05.

So, we reject the null hypothesis, and we use Normal distribution for the test.

4 0
2 years ago
An aquarium has a base in the shape of a trapezoid. The base is 90 cm long at the front, 60 cm long at the back, and 30 cm wide
Nonamiya [84]

Answer:

Step-by-step explanation:

First calculate for the area of the trapezoid (the formula is (base + base / 2) x height):

60 cm + 90 cm = 150 cm

150 cm / 2 = 75 cm

75 cm x 30 cm = 2250 cm²

Now 1 cm² = 1 mL and 1000 mL = 1 L

2250 cm² = 2250 mL

2250 mL = 2.25 L

5 0
2 years ago
Parallel lines s and t are cut by a transversal r. Parallel lines s and t are cut by transversal r. Clockwise from top left, the
bearhunter [10]

Answer:

The corresponding angles are:

∠ 1 and ∠ 5

∠ 2 and ∠ 6

∠ 3 and ∠ 7

∠ 4 and ∠ 8

Step-by-step explanation:

When two parallel lines are crossed by another line, the angles in matching corners are called corresponding angles and they are equal in measures

∵ Lines s and t are parallel

∴ s // t

∵ Line r intersects lines s and t

∴ Line r is the transversal

∵ Corresponding angles are formed

- Look to the attached figure

∴ ∠ 1 ≅ ∠ 5 ⇒ corresponding angles

∴ ∠ 2 ≅ ∠ 6 ⇒ corresponding angles

∴ ∠ 3 ≅ ∠ 7 ⇒ corresponding angles

∴ ∠ 4 ≅ ∠ 8 ⇒ corresponding angles

The corresponding angles are:

∠ 1 and ∠ 5

∠ 2 and ∠ 6

∠ 3 and ∠ 7

∠ 4 and ∠ 8

4 0
1 year ago
Read 2 more answers
Helpmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
alexandr402 [8]

Answer:

  B.  1.2×10^-3 mm

Step-by-step explanation:

What constitutes an "appropriate" unit depends on the use of the number. Since we're not told of any particular use, we might choose the smallest of the available units: mm.

  1.2×10^-3 mm

_____

<em>Additional comment</em>

The most appropriate unit would be the one that eliminates the power-of-ten multiplier:

  = 1.2 µm

6 0
2 years ago
Other questions:
  • Mike has coffee worth $4 per pound that he wishes to mix with 20 pounds of coffee worth $7 per pound to get a mixture that can b
    5·1 answer
  • Javier wants to inscribe a circle inside of the triangle ABC shown in the following figure. He begins by constructing the angle
    9·1 answer
  • All I need is this answer,please help!!
    12·1 answer
  • In a batch of 100 cell phones, there are, on average, 5 defective ones. if a random sample of 30 is selected, find the probabili
    5·1 answer
  • The curve produced by the water coming from a fountain is sketched on the graph.
    5·2 answers
  • Tran has a credit card with a spending limit of $2000 and an APR (annual percentage rate) of 12%. During the first month, Tran c
    12·1 answer
  • A. The average yearly salary of a lawyer is $24 thousand less than twice that of an architect.
    12·1 answer
  • Mean of 7.2,8.5,7.0,8.1,6.7
    11·2 answers
  • Lindsey Smith was the top scorer in a women's professional basketball league for the 2006 regular season, with a total of 867 po
    14·1 answer
  • Kay needs to fix part of her fence.She can buy 6 feet of fencing for $32.00 at a fencing store or 10 feet of fencing for $52.50
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!