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3 years ago

Write a proportion to find how many points x a student needs to score on a test worth 50 points to get a test score of 40%.

Mathematics

1 answer:

Amiraneli [1.4K]3 years ago

3 0

Answer:

20 pts

Step-by-step explanation:

50 points corresponds to a 100% grade. How many points (x) correspond to a 40% grade?

x 40%

------------ = ---------

50 pts 100%

Then 100x = 2000, and so x = 20.

A score of 20 points would correspond with a test score of 40%.

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A person on tour has dollar 360 for his daily expenses. If he extends his tour for 4 days, he has to cut down his daily expenses

mash [69]

Answer:

The original duration of the tour = 20 days

Step-by-step explanation:

Solution:

Total expenses for the tour = $360

Let the original tour duration be for $x$ days.

So, for $x$ days the total expense = $360

Thus the daily expense in dollars can be given by = $\frac{360}{x}$

Tour extension and effect on daily expenses.

The tour is extended by 4 days.

Tour duration now = $(x+4)$ days

On extension, his daily expense is cut by $3

New daily expense in dollars = $(\frac{360}{x}-3)$

Total expense in dollars can now be given as: $(x+4)(\frac{360}{x}-3)$

Simplifying by using distribution (FOIL).

$(x.\frac{360}{x})+(x(-3)+(4.\frac{360}{x})+(4(-3))$

$360-3x+\frac{1440}{x}-12$

$348-3x+\frac{1440}{x}$

We know total expense remains the same which is = $360.

So, we have the equation as:

$348-3x+\frac{1440}{x}=360$

Multiplying each term with $x$ to remove fractions.

$348x-3x^2+1440=360x$

Subtracting $348x$ both sides

$348x-348x-3x^2+1440=360x-348x$

$-3x^2+1440=12x$

Dividing each term with -3.

$\frac{-3x^2}{-3}+\frac{1440}{-3}=\frac{12x}{-3}$

$x^2-480=-4x$

Adding $4x$ both sides.

$x^2+4x-480=-4x+4x$

$x^2+4x-480=0$

Solving using quadratic formula.

For a quadratic equation: $ax^2+bx+c=0$

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Plugging in values from the equation we got.

$x=\frac{-4\pm\sqrt{(4)^2-4(1)(-480)}}{2(1)}$

$x=\frac{-4\pm\sqrt{16+1920}}{2}$

$x=\frac{-4\pm\sqrt{1936}}{2}$

$x=\frac{-4\pm44}{2}$

So, we have

$x=\frac{-4+44}{2}$ and $x=\frac{-4-44}{2}$

$x=\frac{40}{2}$ and $x=\frac{-48}{2}$

∴ $x=20$ and $x=-24$

Since number of days cannot be negative, so we take $x=20$ as the solution for the equation.

Thus, the original duration of the tour = 20 days

6 0

3 years ago

Please answer correctly

Lubov Fominskaja [6]

Answer:

for the question all the way on the bottom, for the pizza everyone paid 2.59$ each

5 0

3 years ago

Read 2 more answers

An article gave the following summary information for fracture strengths (MPa) of n = 196 ceramic bars fired in a particular kil

Oliga [24]

Answer:

54.80 MPa to 55.92 MPa

Step-by-step explanation:

Sample mean fracture strength (x) = 55.36 MPa

Sample standard deviation (s) = 3.99 MPa

Sample size (n) = 196.

The upper and lower bounds for a 95% confidence interval are given by:

$U=x+1.960*\frac{s}{\sqrt{n}} \\L=x-1.960*\frac{s}{\sqrt{n}}$

The upper and lower bounds of the confidence interval are;

$U=55.36+1.960*\frac{3.99}{\sqrt{196}}\\U= 55.92\\L=55.36-1.960*\frac{3.99}{\sqrt{196}}\\L= 54.80\\$

The 95% confidence interval for true average fracture strength is 54.80 MPa to 55.92 MPa

4 0

4 years ago

Find the percent of change from the first value to the second. 72: 81 -

nordsb [41]

Answer:

+12.5%

Step-by-step explanation:

This is rather simple. Subtract 72 from 81, then put the difference over 72. Then, multiply that by 100.

(81 - 72)/72 * 100

Subtract 72 from 81 to get 9

9/72 * 100

Multiply 9 by 100 to get 900

900/72

Simplify the above fraction by cancelling out 9.

100/8

Divide 100 by 8 to get 12.5%

The percent of change is +12.5%

5 0

3 years ago

A quote website includes a "Surprise me!" button that randomly selects a quote from its database. For every 4 quotes in the data

Damm [24]

Answer: 4 quotes

3.5 quotes

Step-by-step explanation:

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3 years ago