Karen is buying pens and pencils for the new school year. She wants to have no more than 25 writing utensils in all. She also wants the number of pencils to be greater than or equal to the square of 3 less than the number of pens. Create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.
The correct answer is 58 viable solutions.
To model the given situation, we need to define variables, create inequalities, and then solve the system of inequalities.
Let x = the number of pens, and y = the number of pencils.
Given information:
- The total number of writing utensils must be less than or equal to 25.
- The number of pencils must be greater than or equal to the square of (3 less than the number of pens).
Step 1: Create the first inequality for the total number of writing utensils.
x + y ≤ 25
Step 2: Create the second inequality for the condition on the number of pencils.
y ≥ (x - 3)^2
Step 3: Solve the system of inequalities.
We can substitute different values of x into the second inequality to find the corresponding values of y.
For x = 1, y ≥ (-2)^2 = 4
For x = 2, y ≥ (-1)^2 = 1
For x = 3, y ≥ 0^2 = 0
For x = 4, y ≥ 1^2 = 1
For x = 5, y ≥ 2^2 = 4
...
Substituting these values into the first inequality, we get:
1 + y ≤ 25 (y ≥ 4)
2 + y ≤ 25 (y ≥ 1)
3 + y ≤ 25 (y ≥ 0)
4 + y ≤ 25 (y ≥ 1)
5 + y ≤ 25 (y ≥ 4)
...
Therefore, the viable solutions are:
(x, y) = (3, 0), (3, 1), (3, 2), ..., (3, 22)
(x, y) = (4, 1), (4, 2), ..., (4, 21)
(x, y) = (5, 4), (5, 5), ..., (5, 20)
There are a total of 22 + 20 + 16 = 58 viable solutions.
Which modified box plot represents the data set?
10,12,2,4,24,2,7,7,9
Answer with explanation:
The Data Set is→ 10,12,2,4,24,2,7,7,9
Arranging the data in ascending order
2,2,4, 7,7,9,10, 12, 24
Number of observation is odd,
So, Median
[tex]\frac{9+1}{2}=5^{th} Observation[/tex]
5th Observation = 7
[tex]Q_{1}[/tex]
=First Quartile of data set that is from first variate to Median value
={2,2,4,7,7}
So, [tex]Q_{1}=4[/tex]
[tex]Q_{3}[/tex]
=Third Quartile of data set that is from last variate to Median value
={7,9,10,12,24}
So, [tex]Q_{3}=10[/tex]
Minimum value in data set = 2
Maximum value in data set = 24
Plotting the Box plot
Option C , is correct Box plot.
Answer: The answer is C
Step-by-step explanation:
which sets of side lengths could form a triangle? Choose all that apply A. 3 centimeters,4 centimeters,9 centimeters B. 3 centimeters, 6 centimeters,9 centimeters C. 4 centimeters, 5 centimeters, 9 centimeters D. 4 centimeters, 6 centimeters, 9 centimeters E. 5 Centimeters, 5 centimeters, 9 centimeters
To solve this question we will have to make use of the triangle inequality which states that "the sum of the lengths of any two sides of a triangle must be greater than the length of the third side".
Let us now use this inequality to check Part A to Part E.
Part A: [tex] 3+4\ngtr9 [/tex] therefore, triangle is not possible
Part B: [tex] 3+6\ngtr9 [/tex] therefore, triangle is not possible
Part C: [tex] 4+5\ngtr9 [/tex] therefore, triangle is not possible
Part D: [tex] 4+6>9, 4+9>6, 6+9>4 [/tex] As all the three sides adhere to the triangle inequality, a triangle is possible with these dimensions.
Part E: [tex] 5+5>9, 5+9>5, 9+5>5 [/tex] As all the three sides adhere to the triangle inequality, a triangle is possible with these dimensions.
Thus, only Options D and E apply
Pia printed two maps of a walking trail. The length of the trail on the first map is 8 cm. The length of the trail on the second map is 5 cm.
(a) 1 cm on the first map represents 3.5 km on the actual trail. What is the scale factor from the map to the actual trail? What is the length of the actual trail according to the first map?
(b) A landmark on the first map is a triangle with side lengths of 3 mm, 4 mm, and 6 mm. What is the scale factor from the first map to the second map? What are the side lengths of the landmark on the second map?
please show your work.
If it takes one hour to fill a pool with 50 ft^3 of water, how many hours will it take to fill a pool that measures 10 ft by 8 ft with a depth of 5 ft?
Answer:
8 hours
Step-by-step explanation:
10 x 8 x 5 = 400. 400 / 50 = 8. So it will take 8 hours to fill a pool with 400ft3
Mr. Macady has an old cylindrical grain silo on his farm that stands 25 feet high with a diameter of 10 feet. Mr. Macady is planning to tear down the old silo and replace it with a new and bigger one. The new cylindrical silo will stand 30 feet high and have a diameter of 15 feet.
A. What is the volume of the old silo
B. What is the volume of the new silo
C. How much greater is the volume of the new silo than the old silo
The volume of the old silo is 1962.5 cubic feet, the volume of the new silo is 5298.75 cubic feet and about 3336.25 greater is the volume of the new silo than the old silo.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Mr. Macady has an old cylindrical grain silo on his farm that stands 25 feet high with a diameter of 10 feet.
h=25 feet and r =5 feet
Volume of cylinder = πr²h
=3.14×5²×25
=3.14×25×25
Volume =1962.5 cubic feet.
Now let us find the volume of new cylinder which has height 30 feet and diameter is 15 feet
Radius =15/2
r=7.5
Volume = 3.14× (7.5)² × 30
=3.14×56.25× 30
V=5298.75 cubic feet
Now let us find how much the new volume of silo is greater than old silo.
Difference = 5298.75 - 1962.5
=3336.25
Hence, the volume of the old silo is 1962.5 cubic feet, the volume of the new silo is 5298.75 cubic feet and about 3336.25 greater is the volume of the new silo than the old silo.
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How many ways are there to choose a card from a deck of cards (52 cards in a deck) and roll a regular 6-sided number cube? 58 52 156 312
NEED HELP!!!!!!
For the following geometric sequence find the recursive formula and the 6th term in the sequence.
{36, 12, 4, ...}
The 6th term is ( 4 / 27 ) and the recursive formula is q = 1/3.
What is geometric progression?When there is a constant between the two successive numbers in the series then it is called a geometric series.
The 6th term of the series is calculated as:-
1st term = 36
2nd term = 12
3rd term = 4
The recursive formula is,
q = 12/36 = 1/3
The 6th term is,
[tex]a_n = a_1( r )^{n-1}[/tex]
[tex]a_6=36 ( \dfrac{1}{3})^5=\dfrac{4}{27}[/tex]
Therefore, the 6th term is ( 4 / 27 ) and the recursive formula is q = 1/3.
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By using double inequality describe all the numbers that are:
a) greater than (−8) but less than (−2)
b) less than 0, but greater than (−5)
c) greater than (−3), but less than 3
First one to answer correctly gets brainliest answer
a) Numbers greater than -8 but less than -2 are represented by the double inequality [tex]\(-8 < x < -2\).[/tex]
b) Numbers less than 0 but greater than -5 are represented by the double inequality [tex]\(-5 < x < 0\).[/tex]
c) Numbers greater than -3 but less than 3 are represented by the double inequality [tex]\(-3 < x < 3\).[/tex]
To describe each set of numbers using double inequalities, we'll define the range of numbers that satisfy each condition.
a) For numbers greater than -8 but less than -2:
[tex]\[ -8 < x < -2 \][/tex]
This double inequality represents all numbers that are greater than -8 on the number line and less than -2, but not including -2 itself.
b) For numbers less than 0 but greater than -5:
[tex]\[ -5 < x < 0 \][/tex]
This double inequality represents all numbers that are less than 0 on the number line and greater than -5, but not including 0 itself.
c) For numbers greater than -3 but less than 3:
[tex]\[ -3 < x < 3 \][/tex]
This double inequality represents all numbers that are greater than -3 on the number line and less than 3, but not including 3 itself.
In summary:
a) Numbers greater than -8 but less than -2 are represented by the double inequality [tex]\(-8 < x < -2\).[/tex]
b) Numbers less than 0 but greater than -5 are represented by the double inequality [tex]\(-5 < x < 0\).[/tex]
c) Numbers greater than -3 but less than 3 are represented by the double inequality [tex]\(-3 < x < 3\).[/tex]
Penelope made a paper chain that was 6 feet, 10 inches long. Anastasia made a paper chain that as 7 feet, 18 inches. If they linked their paper chains together, what would be the combined length? A) 13 feet, 11 inches b) 15 feet, 4 inches c) 19 feet, o inches d) 37 feet, 4 inches
The answer is B, as they both add up to 15 feet and 4 inches
c. Which volume-to-surface-area ratio would be better for an ice cube¡X the lowest possible or the highest possible?
What is the correct answer for number 9
Find the surface area of the sphere to the nearest square unit. Use a calculator.
the inside is 2in
A.13 in.2
B.50 in.2
C.6 in.2
D.3 in.2
Solve for x.
6/59=3/x
[tex]\dfrac{6}{59}=\dfrac{3}{x}\qquad\text{cross multiply}\\\\(6)(x)=(3)(59)\\\\6x=177\qquad\text{divide both sides by 6}\\\\\boxed{x=29.5}[/tex]
given the geometric sequence with the first three terms shown as (2,10,50..) answer the following questions:
Write a recursive definition for the sequence
What is the 10th term of the sequence?
Final answer:
The recursive definition for the given geometric sequence is an = 5an-1, with a1 = 2. Using the geometric formula to find the 10th term, we calculate the 10th term to be 3906250.
Explanation:
The given sequence is a geometric sequence, in which each term after the first is found by multiplying the previous term by a constant ratio. In this case, the ratio is obtained by dividing the second term by the first term. Therefore, the recursive formula for the given geometric sequence is an = 5 × an-1, with the first term a1 = 2.
To find the 10th term of the sequence, we use the formula: an = a1 × r(n-1), where r is the common ratio and n is the term number. Substituting the given values we get a10 = 2 × 5(10-1) = 2 × 59.
Calculating this we find that the 10th term of the sequence is 2 × 1953125 = 3906250.
In Veronica’s art class 5 out of 9 people speak Spanish. What decimal number shows what part of the class speaks Spanish?
For the level 3 course, exam hours cost twice as much as workshop hours, workshop hours cost twice as much as lecture hours. How much are lectures per hour?
Cost of lectures = $7.33 per hour
ExplanationLet [tex]e[/tex] the cost of the exam hours
Let [tex]w[/tex] be the cost of the workshop hours
Let [tex]l[/tex] be the cost of the lecture hours.
We know from our problem that exam hours cost twice as much as workshop, so:
[tex]e=2w[/tex] equation (1)
We also know that workshop hours cost twice as much as lecture hours, so:
[tex]w=2l[/tex] equation (2)
Finally, we also know that 3hr exams 24hr workshops and 12hr lectures cost $528, so:
[tex]3e+24w+12l=528[/tex] equation (1)
Now, lets find the value of [tex]l[/tex]:
Step 1. Solve for [tex]l[/tex] in equation (3)
[tex]3e+24w+12l=528[/tex]
[tex]12l=528-3e-24w[/tex] equation (4)
Step 2. Replace equation (1) in equation (4) and simplify
[tex]12l=528-3e-24w[/tex]
[tex]12l=528-3(2w)-24w[/tex]
[tex]12l=528-6w-24w[/tex]
[tex]12l=528-30w[/tex] equation (5)
Step 3. Replace equation (2) in equation (5) and solve for [tex]l[/tex]
[tex]12l=528-30w[/tex]
[tex]12l=528-30(2l)[/tex]
[tex]12l=528-60l[/tex]
[tex]72l=528[/tex]
[tex]l=\frac{528}{72}[/tex]
[tex]l=\frac{22}{3}[/tex]
[tex]l=7.33[/tex]
Cost of lectures = $7.33 per hour
Fill in the blanks to solve the Pollution Problem.
• What do you want to know?
When the pollution level in the lake will reach 50 tons
• What do you know?
The exponential growth function that models the
problem is P(t) = 3 • e^0.0866t, where P(t) = the number
of tons of ________ in the lake t ________ after 1970.
Pythagorean Theorem
Is this a right triangle?
a = 15 b = √207 c = 12√3
*Please Explain!!*
30% of the employees at a company picnic ate a hot dog for lunch. If 18 employees ate a hotdog, how many people were at the picnic?
A) 20
B) 30
C) 60
D) 90
The area of a rectangle or a 48 square inches the length is 8 inches what is the measure of its width
The sum of four consecutive integers is -22
Complete the rectangle above. What are the coordinates of the missing vertex?
Select one:
A. (7, 3)
B. (7, 4)
C. (6, 3)
D. (3, 7)
20x+13=53
solve for x, right?? Help??
One positive number is 5 times another number . The difference between the two numbers is 80, Find the numbers.
The two numbers in increasing order are ________ and ______
What is the distance between the points (9, 32) and (9, 17) in the coordinate plane?
Ms.Gartland bought x number of shirts for the new members of her chorus.The cost for x number of shirts,including $3.99 shipping,was $ 77.49.Each shirt cost $12.25.There was no sales tax on this purchase.Which equation could be used to find x?
A 3.99(x+12.25)=77.49
B 3.99x+12.25=77.49
C 12.25(x+3.99)=77.49
D12.25x+3.99=77.49
She bought 'x' number of shirts.
The price of one shirt = 12.25 dollars.
Then total price of all shirts would be '12.25x' dollars.
Given is the shipping charge = 3.99 dollars.
Given is the total bill = 77.49 dollars.
It says no other tax would be charged on this order, so total bill would be sum of total price of all shirts and shipping charges.
Total Bill = Total price of all shirts + Shipping charges.
77.49 = 12.25x + 3.99
Hence, option D is correct i.e. 12.25x + 3.99 = 77.49
Which of the following are monomials?
Check all that apply.
A. x - y
B. 9x
C. 24 + 2x2
D. 2x + 12
E. x20
F. 13
The slope of a line passing through H (-2, 5) is -3/4. Which ordered pair represents a point on this line?
A (6, -1)
B (2, 8)
C (-5, 1)
D (1, 1)
Selena is buying an audio system for her car. She can choose among 3 types of stereos, 4 kinds of speakers, and 2 kinds of amplifiers. Which describes how Selena can show her options?
Answer:
Step-by-step explanation:
d