1answer.
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
dimaraw [331]
3 years ago
6

In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, Erica has s

cored 86, 79, and 85 on the first three. What range of scores on the fourth test will give Erica a C for the semester (an average between 70 and 79, inclusive)? Assume that all test scores have a non-negative value.
Mathematics
1 answer:
schepotkina [342]3 years ago
8 0

Answer:

Erica must score between 30 and 66 to obtain a grade average of C.  

Step-by-step explanation:

We are given the following ion the question:

Erica's score:

86, 79, and 85

To get a grade C, the average score of Erica must lie between 70 and 79.

Formula:

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Let x be the score on fourth test.

Thus, we can write:

70\leq \dfrac{86+79+85+x}{4}\leq 79\\\\280\leq 250+x\leq 316\\280-250\leq x \leq 316-250\\30\leq x\leq 66

Thus, Erica must score between 30 and 66 to obtain a grade average of C.

You might be interested in
A rectangle is to be inscribed in an isosceles right triangle in such a way that one vertex of the rectangle is the intersection
svet-max [94.6K]

Answer:

x  =  2  cm

y  = 2  cm

A(max) =  4 cm²

Step-by-step explanation: See Annex

The right isosceles triangle has two 45° angles and the right angle.

tan 45°  =  1  =  x / 4 - y        or     x  =  4  -  y     y  =  4  -  x

A(r)  =  x* y

Area of the rectangle as a function of x

A(x)  =  x  *  (  4  -  x )       A(x)  =  4*x  -  x²

Tacking derivatives on both sides of the equation:

A´(x)  =  4 - 2*x             A´(x)  =  0            4   -  2*x  =  0

2*x  =  4

x  =  2  cm

And  y  =  4  - 2  =  2  cm

The rectangle of maximum area result to be a square of side 2 cm

A(max)  = 2*2  =  4 cm²

To find out if A(x) has a maximum in the point  x  =  2

We get the second derivative

A´´(x)  =  -2           A´´(x)  <  0   then A(x) has a maximum at  x = 2

5 0
2 years ago
A field is in the shape of a rectangle 5/6 mile long and 3/4 mile wide. What is the area of the field? *
Lynna [10]

Area = length x width

Area = 5/6 x 3/4

= (5x3) / (6x4)

= 15/24

= 5/8 square miles

7 0
3 years ago
Find the first term and the common ratio <br>third term =6 and seventh term= 96​
mamaluj [8]

Answer:

First term a₁ = 3/2 and common ratio r = 2

Step-by-step explanation:

We need to find the first term and common ratio while we are given third term = 6 and seventh term = 96

Since common ratio is required so, the sequence is geometric sequence

The formula used is: a_n= a_1r^{n-1}

We are given: third term = 6 i,e

a_3=a_1r(3-1)\\6=a_1r^2----eq(1)

Seventh term = 96

a_7=a_1r(7-1)\\96=a_1r^6----eq(2)

Dividing eq(2) and eq(3)

\frac{96}{6}=\frac{a_1r^6}{a1r2}\\16=\frac{r^6}{r^2}\\16=r^{6-2}\\=> r^4=16\\Taking \ fourth \ root\\ r=2,-2,2i,-2i\\ \ We \ will \ consider \ only \ positive \ value \ of \ r \ i.e \ \textbf{ r= 2}

So, Common Ratio r = 2

Finding First term using eq(1)

a_3=a_1r^2\\6=a_1(2)^2\\6=a_1(4)\\a_1= \frac{6}{4}\\a_1= \frac{3}{2}

So, First term a₁ = 3/2 and common ratio r = 2

6 0
3 years ago
Which is more, 50,000 millimeters or 5 decameters?
Katena32 [7]

Answer:

Step-by-step explanation:

50,000 mm=5,000 cm=500 decimeter=50 m=5 decameter

so both are equal.

8 0
3 years ago
Graph<br> Y=3/4x - 1/2 <br> Pleaseeeee help!!
Nimfa-mama [501]
I’m not 100% sure kind of a guess but I would x=2/3. Good luck
6 0
3 years ago
Read 2 more answers
Other questions:
  • Write an equation for a rational function with:
    7·1 answer
  • What is 999x999 cause i dont get it
    14·2 answers
  • What is the equation of the line that passes through the point (-2,0) and has a slope of -2
    15·2 answers
  • -2/5 + 1/2 please help guys I really need it
    13·1 answer
  • What is the answer to 9.99999999×9.999999999
    15·1 answer
  • HELP!!! ITS TIMED!!!! Please explain the answer!!
    14·1 answer
  • 142- 132= 14+13 pls do this question for me
    15·2 answers
  • Plzzzz helpppp nowww
    11·1 answer
  • PLZ HELP ME ON THIS!!!!!!
    8·2 answers
  • Tracy invests $1,000 into a mutual fund which
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!