Mathematics High School

Your test scores in one class are 82 and 88. What possible scores can you earn on your next test to have a test average between 85 and 90​, ​inclusive?

Answers

Answer 1
Final answer:

To have a test average between 85 and 90, inclusive, the scores on the next test should be greater than or equal to 85 and less than or equal to 100.

Explanation:

To have a test average between 85 and 90, inclusive, you need to find the possible scores on your next test. Let's assume the score on the next test is x. Then, the average of all three tests can be calculated as (82 + 88 + x) / 3. Now, we can set up an inequality to find the possible values of x:

(82 + 88 + x) / 3 ≥ 85 and (82 + 88 + x) / 3 ≤ 90

Simplifying each inequality, we get:

170 + x ≥ 255 and 170 + x ≤ 270

Subtracting 170 from both sides, we have:

x ≥ 85 and x ≤ 100

Therefore, the possible scores you can earn on your next test to have a test average between 85 and 90, inclusive, are any scores greater than or equal to 85 and less than or equal to 100.

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Related Questions

I am struggling with Parts B and D of this calculus question. I think that Parts A and C are OK. I wonder if Parts B and D require the graph that I drew for Part A?

Answers

For part B, you are correct as far as you've gone. There is no algebraic solution to your equation. A graphing calculator or Newton's Method iteration can get you to a solution fairly quickly.
  a ≈ 1.114157141

For part C, you need to consider your answer. For a=0, the equation is that of a straight line, so there is no inflection point at x=1. For cos(a)=0, there are an infinite number of possible values of [tex]a[/tex] that will put a point of inflection at x=1. As you have noted, a=π/2 is only one of them in the range 0 < a < 4.


For part D, again you have stopped part way to the answer. Consider what values of [tex]a[/tex] will make [tex]a \sin(ax)[/tex] strictly greater than 1. There aren't any. The sine function always crosses zero. This part of the question has no solution.

You play darts with a friend. The board is a circle with a 6-inch radius. The “Bull’s Eye” is a smaller circle in the center of the board with an 0.25-inch radius. You throw darts (small metal arrows) at the board. At the end of six weeks, she has thrown 500 darts. She hit the board every time and hit the Bull’s Eye 1 time If you throw 500 darts, how many times should you expect to hit the Bull’s Eye by random chance? Compare this result to your friend’s result. Is she a skilled player for hitting the bull’s eye or is the result of hers expected?

Answers

The area of the board = πr² = 36 π square inches
Area of the Bull's eyes = πr² = 0.0625 π square inches

If a dart is thrown at random, the probability that it will hit the bull's eye can be calculated as:

Area of Bulls's Eyes divided by Area of Complete Board

So, probability of hitting the bulls'e eye = 1/576 = 0.001736

The friend hit Bull's eye once in a 500 throws. So the probability of hitting the Bull's eyes will be = 1/500 = 0.002

If we compare the two probabilities, they are close to each other. So we can conclude that the friend is not a skilled player and she hit the bull's eye just by chance.

Write an equation of the graph:


y = |x| translated two units downward

Answers

Y = |x| - 2. Nothing too complicated for this transformation

y = |x| - 1 is the answer

ur mom

Bryant collects a set of 20 data representing the lengths of worms he found in the garden. The variance of the set of measurements is 36. What is the standard deviation from the mean? _____ millimeters

Answers

The standard deviation, of a set of 20 data, is 6.

Given:
set of 20 data
variance of 36

Find the standard deviation from the mean.

The formula for the standard deviation is the square root of the variance.

Standard deviation = √36

Standard deviation = 6

Trey's mom planted an 18 feet by 20 feet garden in his back yard. this new garden reduced the area of trey's backyard by 24%. which answer choice best represents the total area of the back yard

Answers

Ok so the answer should be 1500 square feet

The garden area is given by:

[tex] A = (18) * (20)

A = 360
[/tex]

We are looking for the backyard area now.

For this, we make the following rule of three:

360 ---------------------> 24%

x -------------------------> 100%

From here, we must clear the value of x.

We have then:

[tex] x = (100/24) * (360)

x = 1500 ft ^ 2
[/tex]

Answer:

The total area of the back yard is:

[tex] x = 1500 ft ^ 2 [/tex]

Each letter of the alphabet is written on a piece of paper and put in a hat. If a piece of paper is chosen at random, what is the probability that it will be a vowel?

The number of favorable outcomes is .

The number of possible outcomes is .

So P(vowel) = , or about percent.

Answers

Number of favourable outcomes = 5

Number of possible outcomes = 26

P(vowel) = 5/26

Answer: 5/26

The probability of pulling a vowel out of the hat is [tex]\frac{5}{26}[/tex]

The number of favorable outcomes is [tex]5[/tex]

The number of possible outcomes is [tex]26[/tex]

The number of possible outcomes is the size of the sample space.

Since the sample space

[tex]S=\{\text{all the letters of the alphabet in the hat}\}[/tex]

then, the number of possible outcomes is

[tex]|S|=26[/tex]

The number of favorable outcomes is possible number of vowels that can be gotten from the hat. Since the set of vowels

[tex]V=\{a,e,i,o,u\}[/tex]

then, the number of favorable outcomes is

[tex]|V|=5[/tex]

The probability of pulling a vowel out of the hat

[tex]P(V)=\frac{\text{number of favorable outcomes}}{number of possible outcomes}=\frac{5}{26}[/tex]

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Is Part A correct? And can someone please help me with part B? (Highlighted)

Answers

Part A. Your model is as good as any. It is hard to tell if the label needs to include the descriptor (length = 12 ft, for example). Certainly your model is sufficient for Part B.

Part B. The total area is the sum of the areas of each of the 6 faces of the box. Opposite faces are the same area, so you have
  A = 2(LW +WD +LD) = 2(LW +D(L +W))
Subsituting the given dimensions, you get
  A = 2((12 ft)(6 ft) +(3 ft)(12 ft +6 ft))
  A = 2(72 ft² +(3 ft)(18 ft))
  A = 2(72 ft² +54 ft²) = 252 ft²

The least amount of paper required to cover the box is 252 ft².

The number of assists per match for the setter on your school's volleyball team has a mean of 58 and a standard deviation of 7. if in the last game he made 77 assists, how many standard deviations is that from the mean? 1.36 standard deviations below the mean 2.71 standard deviations above the mean 1.36 standard deviations above the mean 2.71 standard deviations below the mean

Answers

Given that mean=58
standard deviation=7
thus
77 is (77-58)=18 away from 58
This will be:
19/7=2.71

standard deviations from the mean.

Answer: 2.71 standard deviations above the mean

Answer:

(B)

Step-by-step explanation:

It is given that The number of assists per match for the setter on your school's volleyball team has a mean of 58 and a standard deviation of 7.

Also,  in the last game he made 77 assists, therefore

[tex]77-58=19[/tex] assists away from the mean.

Thus, To get the number of standard deviation that 77 is from the mean, we get the z-score which is given as:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Substituting the given values, we get

[tex]z=\frac{77-58}{7}[/tex]

[tex]z=\frac{19}{7}[/tex]

[tex]z=2.71[/tex]

Thus, there are 2.71 standard deviations above the mean.

Hence, option B is correct.

Compute the sales tax on the following transactions. An article retails for $37.50. The city sales tax is 6%, and the federal excise tax is 8%. How much does the article cost altogether?

Answers

First you must find the rate of both taxes. Since its 8% and 6%, you must add them both together, then divide them by 100. 

14/100 = .14

Then for both rates you must add 1 because it is a tax increase.

1 + .14 = 1.14

Finally times 37.50 with 1.14

37.50(1.14) = 42.75

$42.75 is the answer.

 
Answer:

The article will cost altogether:

                       $ 42.75

Step-by-step explanation:

It is given that:

The  retail price of the article is: $ 37.50.

Also, the article will hold a city tax of 6% and a federal excise tax of 8%.

Hence, the total percent tax on article is: 6+8=14%

This means that the cost price of the article is:

Retail Price of article+14% of retail price.

=  37.50+14% of 37.50

= 37.50+0.14×37.50

= 37.50+5.25

= 42.75

           Hence, the article will cost:  $ 42.75

The greatest common factor of 24and 36 is the least common multiple of a pair of numbers.which two number could they be ? Pls make sure to explain this specifically!!
A.3 and 6
B.4 and 6
C.8 and 9
D.8 and 12

Answers

4, and 6. Because 4 is a common factor of 24, and it is also the least factor. Same thing with 36. Remember: 4 x 6 = 24 and 6 x 6 = 36. Hope this helps!


The measure of arc QS is (4x – 18)°.

What is the value of x?

40.5
49.5
94.5
180



ANSWER IS 49.5

Answers

Answer:

Option B. 49.5 degrees

Step-by-step explanation:

Given that arc QS measures 4x-18

Arc QS is a semicircle and hence subtended angle by semicircle at the centre is 180 degrees.

Use this to find the value of x

4x-18 = 180 degrees

Add 18 to both sides

4x=198

Divide by 4

x =198/4 =49.5

So answer is option B

49.5 degrees

Answer:

49.5

Step-by-step explanation:

Please help me with this

Answers

Number of Art 2 students who entered digital pieces = 24
%( Art 2 students who entered digital pieces)=(24/300)*100%=8%
Number of all entries that were painted by Art 1 students = 34
%( painted by Art 1 students)=(34/300)*100%≈11.3%
%( clay pieces by Art 3 students)= (20/300)*100%=6.7%

From least to greatest,
6.7% - clay pieces by Art 3 students
8%- Art 2 students who entered digital piece
11.3%-painted by Art 1 students


Isabel divided 32 by 8 and got 4. She says that if she divides 32 by 4,the quotient will be greater than 4. Is she correct? Explain.

Answers

Yes, she is absolutely correct because 32/4=8 

8>4 so it make sense.

Find the geometric mean of 125 and 5.

Answers

The geometric mean would have to be 25.

Factor x2 – 8x + 15.
Which pair of numbers has a product of ac and a sum of b?

Answers

-5 and -3 are your numbers. 

The length of a rectangular floor is 2 feet more than its width. The area of the floor is 168 square feet. Kim wants to use a rug in the middle of the room and leave a 2-foot border of the floor visible on all sides. What should the length (the longer side) of the rug be?

Answers

if the area is 168& the length is 2 feet more so length is 14& width is 12 (14*12= 168), the rug is 8feet in total less from all sides so it gives an area on 160. To come out with length& width knowing the length should be less than 14, so it could be either (10*16, 8*20)

Graph BCD with vertices.

Answers

first you need to plot the coordinates given first (along the corridor, up the stairs if you forget which order the directions come in) then join them together.

when you've drawn that, draw on the line x=1

to draw that go to the x axis and go along one, then flip the triangle as though it were in a mirror (use a real mirror if it helps you visualize)

Two rafts are traveling In opposite directions on a straight river. The raft going with the current is traveling at a speed of 12 mph. The raft going against the current is traveling at a speed of 70 miles per hour. Both rafts travel the river for two hours. Which equation represents the situation? Assume the raft traveling with the current travels X miles in the raft traveling against the current travels y miles.

A. 12/x - 7/y = 1/2
B. 12x + 7y = 2
C. x/12 - y/7 = 2
D. x/12 + y/7 = 4
E. 12x + 7y = 4

Answers

Time =(distance)/speed
Time taken by the raft going with the current to travel x miles is:
12/x hours
Time taken by the raft going against the wind is:
7/y
Total time taken for both raft is 4 hours thus:
12/x+7/y=4
hence the answer is:
D. x/12 + y/7 = 4

The path of a rocket ship is given by the parametric equations x(t)=3t and y(t)=4t^2+1, where t is the time in seconds after launch. Where is the ship after 10 seconds?
A.) (3,4)
B.) (3,5)
C.) (30,401)
D.) (30,501)

Answers

For this case we have the following equations that represent the position of the rocket:
 x (t) = 3t
 y (t) = 4t ^ 2 + 1
 Substituting t = 10 in both equations we have:
 x (10) = 3 (10) = 30
 y (10) = 4 (10) ^ 2 + 1 = 400 + 1 = 401
 Therefore, the position of the rocket is:
 (x, y) = (30, 401)
 Answer:
 the ship after 10 seconds is at:
 C.) (30,401)
The answer is C. (30,401) I already checked. 

How to find an area of a circumbscribed hexagon using the diameter?

Answers

The formula for the area of a circumscribed hexagon  = 1/2 * 6 * a * r    where a = side length and r = radius of the circle  ( = 1/2 the diameter)  so in terms of the diameter and side length its 1/2 * 1/2 * 6 *d * a  =   1.5 ad.

You can calculate the value of a  by using trigonometry  You consider one of the 6 isosceles triangles that make up the hexagon. The vertex angle of these triangles = 60 degrees so:-

tan 30  =  1/2 a /  r  =  1/2 a / 1/2 d  = a/d

a =  d tan 30  = sqrt3 d / 3

Substituting for a :- 

So the  required formula for the area of the hexagon = 1.5 ad 

= 1.5 * sqrt3 d * d / 3  =  1/2 sqrt3 d^2   Answer

Finish the pattern, 1, 2, 6, 22, __, __?

Answers

The pattern is times 4, minus 2. So, 22 x 4 = 88-6 = 86, then 86 x 4 = 344-2 = 342
So,
1, 2, 6, 22, 86, 342 is your answer
I think the pattern goes like this 1, 2, 6, 22, 86, 342 

the distance between bay town and oak glen is 175 miles. if the equation y=-x+175 represents the distance left to travel to oak glen, what does the domain represent? what is the domain?

a) time left to reach oak glen; x>0
b) distance left to reach oak glen; x>0
c) time it takes to travel oak glen; x>0
d) distance traveled since leaving bay town; x>0

Answers

The domain is
the distance traveled since leaving bay town; x>0.

The set of input values is distance traveled and it will make the 175 miles decreaxse.

The correct option is D, distance traveled since leaving bay town; x>0.

What is the domain and range of a function?

The domain of a function is the set of x values for which it is defined, whereas the range is the set of y values for which it is defined.

Given that the distance between bay town and oak glen is 175 miles. If the equation y=-x+175 represents the distance left to travel to oak glen.

Since the distance left to travel to oak glen can be 0 this will be when you reach Oak glen, while the minimum will be when the journey is just started and you haven't travelled even a single mile.

Therefore, the domain of the function is from 0 to 175, and the domain represents the distance traveled since leaving the bay town.

Hence, the correct option is D, distance traveled since leaving bay town; x>0.

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A test consists of 10
a. True
b. False questions. to pass the test a student must answer at least 9 questions correctly. if a student guesses on each question, what is the probability that the student will pass the test?

Answers

the answer will be 1/2^9

a man made lake is stocked with 10,000 fish. This population is expected to decline by an annual rate of 15%. Predict the fish population 5 years after the lake is stocked

Answers

I got 2,500 left after 5 years.
10,000*15% = 1,500 or you could do 10,000*.15 = 1,500

That is a loss of 1,500 fish per year.
If you want to think of this as a proportion then you would do
Year/fish lost

1/1,500 = 5/x
X=5*1,500
X=7,500

The population of the fish after 5 years equals
10,000-7,500 = 2,500
So your answer is 2,500 fish are left

The population will be approximately 4,437 fish after 5 years.

To predict the fish population 5 years after the lake is stocked,

We can use the formula for exponential decay:

[tex]\[ P = P_0 \times (1 - r)^t \][/tex]

Where:

P is the final population[tex]\( P_0 \)[/tex] is the initial populationr is the annual rate of decline (expressed as a decimal)t is the number of years

Given:

[tex]\( P_0[/tex] = 10,000  (initial population)r = 0.15  (annual rate of decline, expressed as 15% or 0.15)t = 5  (number of years)

Substituting the values into the formula:

[tex]\[ P = 10,000 \times (1 - 0.15)^5 \][/tex]

[tex]\[ P = 10,000 \times (0.85)^5 \][/tex]

Calculating:

P ≈ 10,000 × 0.443705

P ≈ 4437.05

So, the fish population 5 years after the lake is stocked is approximately 4437 fish.

What is the total amount and the amount of interest earned on $6,500 at 6% for 25 years?

Answers

Here's the equation for one year:
0.06(6500) + 6500
But because it is 25 years:
25(0.06(6500)) + 6500
1.5(6500) + 6500
We can make it simpler:
2.5(6500)
The total amount is $16350

To calculate the total amount and interest earned on $6,500 at 6% simple interest for 25 years, you use the formula I = P × r × t, which gives you interest (I) of $9,750. Adding the interest to the principal, the total amount after 25 years is $16,250.

To calculate the total amount and the interest earned on $6,500 at a simple interest rate of 6% for 25 years, we can use the simple interest formula:

I = P × r × t

Where:

I is the interestP is the principal amount ($6,500)r is the annual interest rate (6%, or 0.06)t is the time in years (25)

Using this formula:

I = $6,500 × 0.06 × 25

I = $9,750

The total amount after 25 years will be the principal plus the interest:

Total Amount = P + I

Total Amount = $6,500 + $9,750

Total Amount = $16,250

The interest earned on the investment after 25 years is $9,750.

1. In the figure, m DE = 106 degrees and m BC = 62 degrees. The diagram is not to scale.

What is m< A?

A) 44 degrees

B) 22 degrees

C) 75 degrees

D) 85 degrees


2. In the figure, m AB = 45 degrees and m CD = 23 degrees. The diagram is not drawn to scale.

What is the value of x?

A) 34 degrees

B) 56.5 degrees

C) 22 degrees

D)68 degrees


Can someone please check my work and tell me if I'm correct or not and explain.

Answers

For question 1, the formula for that is m1= 1/2(a-b). 106 being A and 62 being B. You should get m1=.5*(106-62) which equals B.22

The measure of the missing angles in both instances is; m∠A = 22 degrees and x = 34 degrees

How to find the angles in the triangle?

1) For question 1, the formula for the missing angle from triangle is;

m∠A = ¹/₂(∠DE - ∠BC).

Thus;

m∠A = ¹/₂(106 - 62).

m∠A = 44/2

m∠A = 22 degrees

2) To get the missing angle, we will use the formula;

x = ¹/₂(AB + CD)

This is because the measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

x = ¹/₂(45 + 23)

x = 34 degrees

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A tree's root is 9 feet below ground and spans a radius of 6 feet. If the total length of the tree from root tip to top is 23 feet, what is the tree's elevation above ground?
a. 14 feet
b. 17 feet
c. 26 feet
d. 32 feet

Answers

Hello!

You know the tree goes 9 feet underground and the tree is 23 feet tall from root to top

You can subtract how far the tree goes underground by the length of the tree to get the answer

23 - 9 = 14

The answer is A) 14 feet

Hope this helps!

which statement most accurately explains why x^5/x^2 is equal to x^3?

Answers

[tex]\bf \cfrac{x^5}{x^2}\implies \cfrac{x^{3+2}}{x^2}\implies \cfrac{x^3\underline{x^2}}{\underline{x^2}}\implies x^3[/tex]
The answer you are looking for would be C.

When you divide varibles with exponents, you subtract the exponents. Since there are no numbers in front of the x, we can assume there is only 1 x. 1x/1x = 1x. Since the top has the largest exponent, you'd subtract the bottom exponent to the top, leaving a power of 3. Thus meaning, the answer of x^3 is explained in C.

I hope this helps!

Elijah is going to spin a spinner 180 times. mc008-1.jpg He predicts that 60 of those spins will result in the spinner landing on the section labeled 3. Based on the theoretical probability, which best describes Elijah’s prediction?

Answers

Answer:

its C on Edge

Answer:c

Step-by-step explanation:

Which graph represents g(x)=(x−3)2−5 ?

Answers

The graph has vertex (3, -5),
and it is looking upward because it is positive coefficient in front of (x-3)²
Correct answer is A.
Final answer:

The graph of g(x) = (x-3)^2 - 5 is a parabola that opens upwards. The vertex is located at (3, -5) and the function values are negative when x is less than 3.

Explanation:

The graph of the equation g(x) = (x-3)^2 - 5 is a parabola. The vertex of the parabola is located at the point (3, -5), and the parabola opens upwards because the coefficient of the quadratic term is positive. When x is less than 3, the function values are negative, and when x is greater than 3, the function values are positive.

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