The cost per highlighter is approximately $1.
To find the cost per highlighter, we can use a system of equations. Let's call the cost per highlighter "h" and the cost per pen "p". Then, we can set up two equations based on the information given;
80h + 20p = 120 (day 1)
120h + 40p = 200 (day 2)
We can simplify these equations by dividing both sides by 20;
4h + p = 6 (day 1)
6h + 2p = 10 (day 2)
Now we can use the first equation to solve for p in terms of h;
p = 6 - 4h
Substitute this expression for p into second equation;
6h + 2(6 - 4h) = 10
Simplify and solve for h;
6h + 12 - 8h = 10
-2h = -2
h = 1
Therefore, the cost per highlighter is $1.
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A triangular prism and it’s net are shown below. The top and the bottom of the prism are shaded. All lengths are in centimeters.)
The solution is: the area of the shaded base in square centimeters is:
B= 15 cm²
Here, we have,
The base of the triangular shaped wedge of cheese is a right-triangle.To find the area of a right-triangle you apply the formula for half base by height.
A=1/2*b*h
= base area
= B
In this case, assume the sides of the triangle given are;
a=5 cm and b=6 cm,
thus area will be 1/2*6*5 =15 cm²
Hence, the area of the shaded base in square centimeters is :
B= 15 cm²
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complete question:
Evelyn cut a wedge of cheese into the shape of a triangular prism-like the one shown below. The shaded part represents one of the bases of the prism.
A formula for the volume of a triangular prism is v=Bh . Which equation can be used to find B , the area of the shaded base in square centimeters?
Work out the value of fg^2 when:
f = -5 and g = -4
A car pulls the emergency hand brake, accelerating at -4.0 m/s2 for 7.5 seconds to a complete and total stop. What was the initial velocity of the car before the brake was pulled?
The initial velocity of the car before the brake was pulled is 30m/s
What was the initial velocity of the car before the brake was pulled?From the question, we have the following parameters that can be used in our computation:
A car pulls the emergency hand brake, accelerating at -4.0 m/s2 for 7.5 seconds
This means that
Acceleration = -4.0m/s^2
Time = 7.5 seconds
Using the above as a guide, we have the following:
Initial velocity = -Acceleration * Time
substitute the known values in the above equation, so, we have the following representation
Initial velocity = 4 * 7.5
Evaluate
Initial velocity = 30
Hence, the initial velocity is 30
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What is the base pic attached below
Answer: 2.5
Step-by-step explanation:
the base is always positive, and it says f(x)= 1/2*5^x
1/2*5 is 2.5, so I think the base is 2.5
hope it helped:)
Graph the feasible region and find the values of x and y that give the maximum possible value of g=8x+12y subject to the following constraints.
The feasible region on the attached graph of the inequalities created with MS Excel indicates that the maximum value of g = 8·x + 12·y is 100
What is an inequality?The feasible region is the region on the graph of the inequalities that satisfies the specified constraints.
The specified equations obtained from the constraints in slope intercept form are;
y = -0.5·x + 7; The region below the graph is shaded
y = -0.75·x + 9; The region below the graph is shaded
x = 0; The region to the right of the line x = 0 is shaded
y = 0; The region above the line y = 0 is shaded
The point of intersection of the graphs can be found from the equation; -0.5·x + 7 = -0.75·x + 9
Which indicates that at the intersection, x = 8, and y = -0.5×8 + 7 = 3
The corner points are; (0, 0), (0, 7), (8, 3), (12, 0)
The value of the function g for each of the feasible region are therefore;
g(0, 0) = 8 × 0 + 12 × 0 = 0
g(0, 7) = 8 × 0 + 12 × 7 = 84
g(8, 3) = 8 × 8 + 12 × 3 = 100
g(12, 0) = 8 × 12 + 12 × 0 = 96
The maximum possible value of g therefore is 100, which is the value at the point (8, 3)Please find attached the graph of the inequalities showing the feasible region created with MS Excel
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bao mom is picking him up from the ice rink she is at home which is located at the origin (0,0) how many total units is the ice rink away from the origin explain
The total units of length for the ice rink away from the origin is 14.42 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
Note: Ice rink is located at point (12, 8).
By substituting the given end points into the distance formula, we have the following;
Distance = √[(12 - 0)² + (8 - 0)²]
Distance = √[(12)² + (8)²]
Distance = √[144 + 64]
Distance = √208
Distance = 14.42 units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
1. Which of the following is a set or not?
(a) A=Set of tall man
(b) B=Set of beautiful women
(c) C=Set of tall students of class 10
(d) D=Set of counting number
(e) E=Set of good students
(f) F=Set of yellow roses
Consider the following triangle. A right triangle. The hypotenuse is 5 feet, the side opposite to angle theta is 3 feet, the side adjacent to angle theta is 4 feet. If sin Theta = three-fifths, what is the measure of the angle? a. 53.1º b. 36.9º c. 30.1º d. 59º
The measure of the angle is 36.9^o. Option B.
What is a right triangle?A right triangle is a form or type of triangle in which the measure of one of its internal angles is 90^o. As such, either the trigonometric functions or Pythagorean theorem can be applied to determine any of its properties as the case may be.
From the details given in the question, we can deduced that;
Sin θ = 3/5
= 0.6
So that,
θ = Sin^-1 0.6
= 36.87
θ = 36.9^o
The measure of the angle is 36.9^o. Option B.
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ACTIVITY 2: Simplify the following.
The index forms are simplified to;
1. [tex]5^6^\sqrt{2}[/tex]
2.[tex]3^5\sqrt{3}[/tex]
3. [tex]2^2^\sqrt{25}[/tex]
How to simply the index formsIt is important to note the following about the rules of index forms;
Add the exponents when multiplying index forms of like basesSubtract the exponents when dividing index forms of like basesExponents of unlike bases cannot be add or subtracted.From the information given, we have that;
[tex]5^\sqrt{2}[/tex] × [tex]5^\sqrt{50}[/tex]
Add the exponents, we have;
[tex]5^\sqrt{2} ^+ 5\sqrt{2}[/tex]
Then, we have;
[tex]5^6^\sqrt{2}[/tex]
2. [tex]3\sqrt{12}[/tex] × [tex]3^\sqrt{27}[/tex]
We have;
[tex]3^2^\sqrt{3} + 3\sqrt{3}[/tex]
Add the exponents
[tex]3^5\sqrt{3}[/tex]
3. [tex]2^2^\sqrt{25}[/tex]
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using the table feature of a graphing utility what would be the intensity of an earthquake with an amplitude of 200,000 micrometers for 0.5 seconds?
Using the table feature of a graphing utility the intensity of an earthquake with an amplitude of 200,000 micrometers for 0.5 seconds would be 2.16 x 10¹⁴ joules/second/meter².
How did we get this ?First, note that the intensity of an earthquake with an amplitude of 200,000 micrometers for 0.5 seconds can be calculated using the formula..
I = (1/2)ρv²
Here I Intensity
ρ = density of the medium - this is a constatnt
v = velocity of the S-waves
If we used a graphing tool
a coumun ffor v will be created
a column for the formula for velocity will also be created.
The formula for velocity is
V = A/ T
A = amplitude
T = time or period in seconds
Since A = 200,000 micrometers; and
T = 0.05 secons
v = 200,000 / 0.5
v = 400,000 micrometer/sec
Back o the table, we ahve to add another oclumn for V²
then enter the values for V²
V² = 400,000²
v² = 160,000,000,000 micrometer²/sec²
Nowe we add another column which is
I = 1/2(pv²)
I = 2.16 x 10¹⁴ joules/second/meter².
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‼️HELP CUZ IM SO LOST PLEASE‼️
Using two column proof we have been able to show that AB ║ EC
by definition of alternate interior angles
How to use two column proof?A two-column proof is defined as a two-column table labeled with statements on the left-hand side and reasons on the right-hand side.
The two column proof of the given diagram is as follows:
Statement 1: ΔADE is an Isosceles Triangle
Reason 1: Given
Statement 2: ∠DEA ≅ ∠DAE
Reason 2: Properties of Isosceles Triangles
Statement 3: ∠ADE = 20°
Reason 3: Sum of angles in a triangle
Statement 4: ∠BAD ≅ ∠EDA
Reason 4: Congruent Angles
Statement 5: ∠BAD and ∠EDA are alternate angles
Reason 5: Alternate angles are congruent
Statement 6: AB ║ EC
Reason 6: Definition of alternate interior angles
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How can you quickly know that a function is a growth function?
Answer:
3rd choice: when b>1
Step-by-step explanation:
For this function, a is the starting value (initial amount). b is the decay or growth factor. If b>1, then the function is a growth function.
FYI, if 0 < b < 1, then it is a decay function.
Can someone help me find if the function is increasing or decreasing and why the c intercept is (look at the photo)
Using the information in the table, how many milliliters are in 7 kiloliters?
7,000 mL
700,000 mL
kiloliters (KL) liters (L) milliliters (ml)
3
4
5
3,000
4,000
5,000
3,000,000
4,000,000
5,000,000
70,000 mL
7,000,000 mL
Answer:
7e+6
Step-by-step explanation:
biggest answer
Find the circumference and the area of a circle with radius 4 m.
Use the value 3.14 for , and do not round your answers. Be sure to include the correct units in your answers.
4m
Circumference:
Area:
prove that:
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)
The given identity (P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1) is proven below
How to prove the given identityGiven the following equation
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)
We start by simplifying the left-hand side of the equation:
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)= [(P²+1)/(P(P-1))] + [(P²+1)/(P(P+1))] - [(P²-1)/((P+2)P)] - [(P²+1)/((P-2)P)]
Next, we have the following steps to simplify the expression
= [(P³ + P² + P + 1)/(P(P²-1))] - [(P³ - 3P)/(P(P²-4))]
= [(P³ + P² + P + 1)(P²-4) - (P³ - 3P)(P²-1)]/[(P(P²-1))(P(P²-4))]
= [(P⁵ - 3P³ + P³ - 3P² + P² - 4P + P² - 4P - 4 + P³ - 3P)/(P⁴ - 5P² + 4)]
= [P⁵ - 2P³ - 6P² - 8P - 4]/[(P²-4)(P²-1)]
= -4(2p² + 1)/(p²-4) (p² - 1)
Hence, the given identity is proven.
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Which statement about a dilation with a scale factor of 3 is true?
O Three is added to each side in the pre-image to find the corresponding side length in the image.
O Three is subtracted from each side in the pre-image to find the corresponding side length in the image.
Each side in the pre-image is multiplied by three to find the corresponding side length in the image.
Each side in the pre-image is divided by three to find the corresponding side length in the image.
Answer:
C is the answer
Given : dilation with a scale factor of 3
To find : Which statement is true
Step-by-step explanation:
Solution: A dilation is a transformation that produces an image that is the same shape as the original, but is a different size
if Dilation factor N then image Size is multiplied by N
if Scale factor < 1 then image get reduced
if scale factor > 1 then image get enlarged
scale factor = 1 lead to Same size image
Here is given that Scale factor of 3
=> image will be enlarged to 3 times the original image
Hence correct option is :
C)Each side in the pre-image is multiplied by three to find the corresponding side length in the image
Answer: C
Step-by-step explanation: Edge Unit Test
A company gives a 12% discount to his customers on retail price. If the total is over $10,000 after the discount, they give an additional 3% discount on the remaining balance. A customer’s total came to $13,500 (discounted price). How much did he save?
Answer:
Therefore, the customer saved $2,448.45.
Step-by-step explanation:
To answer this question, we need to use the percentage discount formula to find the original price and the amount saved.
Let x be the original price of the product. Then, after applying the 12% discount, the price becomes 0.88x. If the total is over $10,000 after this discount, then an additional 3% discount is applied on the remaining balance, which means the final price becomes 0.97 * 0.88x.
We are given that the final price is $13,500, so we can set up an equation and solve for x:
0.97 * 0.88x = 13,500 x = 13,500 / (0.97 * 0.88) x = 15,948.45
Therefore, the original price was $15,948.45.
The amount saved is the difference between the original price and the final price:
15,948.45 - 13,500 = 2,448.45
A sequence can be generated by using gn = 2(gn-1), where g1 = 1/3 and n is a whole number greater than 1.
What are the first 5 terms of the sequence?
The first 5 terms of the sequence are 1/3, 2/3, 4/3, 8/3 ans 16/3
What are the first 5 terms of the sequence?From the question, we have the following parameters that can be used in our computation:
The sequence is generated by using gn = 2(gn-1)
Such that g1 = 1/3 and n is a whole number greater than 1.
Using the above as a guide, we have the following:
The sequence means that we multiply the current term by 2 to get the next term
So, we have the following representations
a(2) = 2 * 1/3 = 2/3
a(3) = 2 * 2/3 = 4/3
a(4) = 2 * 4/3 = 8/3
a(5) = 2 * 8/3 = 16/3
Hence, the first 5 terms of the sequence are 1/3, 2/3, 4/3, 8/3 ans 16/3
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The two-way frequency table shows the results of a survey of students.
Right-handed
Left-handed
Total
In music program Not in music program Total
43
394
437
15
33
48
58
427
475
How many left-handed students are in the music program?
OA. 15
OB. 48
OC. 43
OD. 58
The left-handed students in the music program are option A 15 students.
What is two-way frequency table?A table that shows the frequencies of two category variables is known as a two-way frequency table. It is a method for succinctly and clearly organising and displaying data for two variables. One variable is represented by the table's rows, while the other variable is represented by the table's columns. The frequency of each combination of categories is displayed in the table's cells. To examine the relationship between the two variables and to spot patterns and trends in the data, a two-way frequency table can be employed. To summarise and analyse data, it is frequently used in statistics, the social sciences, and other disciplines.
From the given table the number of students that are in music program and left handed is given by the intersection of the row and column of the two.
Thus, he left-handed students in the music program are 15.
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Work the following problems using the previous tables. Choose the correct answer.
Currency on hand = 2,000 Swiss francs
Currency desired = Dutch guilders (Holland)
How many guilders based on the Wednesday rate? (Hint: Convert 2,000 Swiss francs to United States dollars. Then convert United States dollars into guilders.)
Answers:
2,533.66
2,455.75
2,465.33
The conversion of 2,000 Swiss francs to United States dollars and from United States dollars into Dutch guilders (Holland) based on Wednesday's currency exchange rate is D. ƒ4,032.
What is the exchange rate?The exchange rate represents the unit rate at which one currency is exchanged for or converted to another.
Exchange rate conversions rely on the mathematical operations of division or multiplication.
1 CHF = $1.12
2,000 CHF = $2,240 ($1.12 x 2,000 CHF)
On Wednesday April 26, 2023, $1.00 = ƒ1.80
$2,240 = ƒ4,032 ($2,240 x ƒ1.80)
Thus, we can conclude that 2,000 CHF (Swiss francs) are worth 4,032 Dutch guilders.
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At Wynne College, there are 240 students in Year 12.
The interquartile range of the times taken for these students to travel to college is 32 minutes.
How many of these students have travel times within this interquartile range?
About 120 students have travel times within the quoted interquartile range.
InterquartileThe interquartile range (IQR) represents the range of the middle 50% of a set of data, which is the difference between the third quartile (Q3) and the first quartile (Q1).
Assuming that the travel times are normally distributed and that we have information on the quartiles, we can use the formula:
IQR = Q3 - Q1
To find the number of students whose travel times fall within the interquartile range, we need to know the values of Q1 and Q3.
Since the IQR is 32 minutes:
32 = Q3 - Q1
We also know that the total number of students in Year 12 is 240. Assuming that all students have reported their travel times, we can use the interquartile range to estimate the proportion of students whose travel times fall within this range.
If the interquartile range covers the middle 50% of the data, then each quartile should cover 25% of the data. Therefore, we can estimate that the number of students whose travel times fall within the interquartile range is:
Number of students = 240 x 0.50 = 120
Therefore, we estimate that 120 of the 240 Year 12 students have travel times within the interquartile range of 32 minutes.
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Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
Answer: X = 25
Step-by-step explanation: Since 36 divided by 2 equals 18, which would cancel out the two on the left side leaving us with. (x - 7) = 18 we can add 7 to both sides to get. X = 25
Edit: To whoever said my math is incorrect is wrong, I even double checked with multiple sources and people. It must’ve been a different equation or number. Sorry for not being able to help, however the math was correct.
Please answer if you know this one with the steps thank you.
Answer: 36600 = E
Step-by-step explanation:
Given:
T=.2 (E - 10600)
T=5200
Find: E
Solution:
>substitute into thequation. You know T=5200
5200 = .2(E-10600) > Divide both sides by .2
26000 = E- 10600 > add 10600 to both sides
36600 = E
Express all real numbers greater than 5 in interval notation.
All real numbers greater than 5 can be expressed in interval notation as:
(5, ∞)
How to express all real numbers greater than 5 in interval notation?Interval notation is a way of representing an interval on a number line. Simply, it is a method of writing subsets of the real number line.
All real numbers greater than 5 can be expressed in interval notation as:
(5, ∞)
Where the round bracket "(" means 5 is not included in the interval, and the infinity symbol "∞" means the interval continues indefinitely to the right.
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help pls I don't understand it bc I'm not smart
Answer: the answer to be smart is to learn
Step-by-step explanation:
if you learn then you can understand the u are not smart
3. Abby has 3 bags of oranges with 14,
23 and 28 oranges in them. Abby
rounds the number of oranges in each
bag to the nearest ten. About how
many oranges does Abby have
altogether?
Answer:
60
Step-by-step explanation:
14 rounds to 10
23 rounds to 20
28 rounds to 30
10+20+30=60
3. Arthur's mother is a mechanical engineer. She is designing
rectangular carts formoving finished goods from a factory's
manufacturing floor to the loading dock, where the goods are placed
on trucks.
She made a drawing showing where the carts must turn from a
hallway 48 inches wide to pass through a doorway 36 inches wide.
The drawing shows the longest cart that will pass through the
doorway.
to manufacturing floor 30 in.
G
E.
to loading dock
B
D
a) What kind of triangles are AABC and ACFD?
cart
36 in.
48 in.
b) In the drawing, one sixth of an inch represents 1 foot. What is the
scale factor of the drawing? Explain.
a) is Right angle Triangles both of them
b) The scale factor is 1:2.
How to solveGiven AFD = 90 degrees, So CFD = 90 degrees.
So it a Right Angle Triangle.
Again ABC = 90 degrees, It's also a Right Angle Triangle.
Here see both the Triangle are opposite to each other so according to the theorem sum of all three angles of a triangle is 180 degrees
so if any angle is 90 deg then the other two sum is also 90 deg.
Given the scale Factor, 1/6 inch = 1 foot,
So it is a Reducing Scale so let 'x' be in inches
So the Scale Factor = 1:2
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The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 150 grams of a
radioactive isotope, how much will be left after 6 half-lives?
Use the calculator provided and round your answer to the nearest gram.
grams
PLS HELP ASAP 90 POINTS Kim and her friends watched the server making smoothies. The table shows the number of mangos that were used for each of the different sizes of smoothies that the friends ordered.
Mangos Used Smoothie Size
Bri 1 7 oz
Kim 3 21 oz
Angela 4 28 oz
Which statement is correct based on the data?
The ratio of smoothie size to mangos used for Kim is 1:7, and the ratio of smoothie size to mangos used for Bri is 3:28.
The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim.
The ratio of smoothie size to mangos used for Bri is 7:1, and the ratio of smoothie size to mangos used for Angela is 4:28.
The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela.
Answer:
The correct statement is "The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela".
The correct answer option is option A
How to solve ratio?
Mangos Used Smoothie Size
Angela 1 9 oz
Kim 3 27 oz
Bri 4 36 oz
Check the given options to determine which statement is correct;
The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela.
Kim = 27 : 3 = 9 : 1
Angela = 9 : 1
True
The ratio of smoothie size to mangos used for Kim is 1:9, and the ratio of smoothie size to mangos used for Bri is 4:27.
Kim = 27 : 3 = 9 : 1
Bri = 36 : 4 = 9 : 1
False
The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim.
Angela = 9 : 1
Kim = 27 : 3 = 9 : 1
False
The ratio of smoothie size to mangos used for Bri is 9:1, and the ratio of smoothie size to mangos used for Angela is 4:36.
Bri = 36 : 4 = 9 : 1
Angela = 9 : 1
False
Therefore, Kim and Angela has equal ratio of smoothie size to mangoes used.