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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what could be the value of the point grafted only number line between 0.09 and 0.10
Write the coordinates of the vertices after a reflection over the x-axis.
y
x
-10
10
-10
10
0
T
U
V
T(-1, 7)
→
T′(
,
)
U(-1, 8)
→
U′(
,
)
V(9, 6)
→
V′(
,
)
T(-1, 7)
→
T′(-1, -7)
U(-1, 8)
→
U′(-1, -8)
V(9, 6)
→
V′(9, -6)
Please Help With Question Inside of the picture
The workers percentile score is given as follows:
69.15%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The z-score for this problem is given as follows:
z = 0.5.
Hence the percentile score is of 69.15%, as z = 0.5 has a p-value of 0.6915.
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What is the area of this figure? 9 cm 2 cm 9 cm 7 cm Submit 4 cm 2 cm 3 cm Write your answer using decimals, if necessary. square centimeters 6 cm Work it out
Therefore , the solution of the given problem of area comes out to be the trapezium has a surface area of 39 square centimetres.
What does an area actually mean?Calculating how much space would be needed for fully covering its exterior will reveal its overall dimensions. The surrounding environment is considered while selecting a comparable product with a rectangular shape. The surface area of anything determines its overall dimensions. The number of sides connecting a cuboid's four trapezoidal shapes determines how much water it can contain.
Here,
We can use the formula for a trapezoid's area if we assume that the shape is a trapezoid with parallel sides that are 9 cm and 4 cm and a height of 6 cm.
=> A = (a + b)h/2
where h is the height, and a and b are the lengths of the parallel sides.
When we enter the values we have, we obtain:
=> A = (9 + 4)(6)/2
=> A = 13(3)
=> A = 39
Consequently, the trapezium has a surface area of 39 square centimetres.
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PLEASE HELP ME QUICK!!!!
Answer:
B. $7.50
Step-by-step explanation:
We know profit or P-----P(n) where n is the quantity/number of the item) is the difference of the revenue-----R(n)-----and the cost-----C(n)
P(n) = R(n) - C(n)
Revenue is
the product of price (p) of the item and, number/quantity (n) of the item:R(n) = pn
Cost is a combination of
fixed costs (represented by a constant (c), as the business or Indvidual making a profit must pay a certain cost, even if they don't make any of their items) and, variable costs (this costs changes depending on the number/quantity of the item and is the product of the marginal cost (m) and the number/quantity (n) of the item)The cost function resembles a linear equation:
C(n) = mn + c
Since we're shown that P = 7.5n - (2.25n + 15), we know that R(n) must be R(n) = 7.5n and C(n) must be C(n) = 2.25n + 15
Thus, we know she charges $7.5 per necklace sold.
If x=3t+t^2 and y=7−2t, find an equation y=mx+b of the tangent to the curve at t=2.
m=
b=
The values of m and b after evaluation is -2 and 23 under the condition that If x=3t+t² and y=7−2t, and tangent to the curve at t=2.
In orde to evaluate the equation of the tangent to the curve at t=2, we have to calculate the slope of the curve at t=2.
The slope of the curve at t=2 is presented by the derivative of y with respect to x at t=2.
y = 7 - 2t
x = 3t + t²
dy/dx = -2
Then, the slope of the tangent to the curve at t=2 is -2.
Now we have to evaluate the point on the curve at t=2.
x = 3(2) + (2)² = 10
y = 7 - 2(2) = 3
So, the point on the curve at t=2 is (10,3).
Applying point-slope form of equation of line:
y - y₁ = m(x -x₁)
Here,
m = slope and (x₁,y1) is a point on the line.
Staging m=-2 and (x₁,y₁)=(10,3),
y - 3 = -2(x - 10)
Applying simplification
y = -2x + 23
Then, the equation of the tangent to the curve at t=2 is y=-2x+23.
So, m=-2 and b=23.
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Trigonometry homework help
The distance between the installations is given as follows:
126.42 miles.
What is the law of cosines?The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is also known as the Cosine Rule.
The Law of Cosines states that for any triangle with sides a, b, and c and angle B opposite to side b, the following equation holds true:
b^2 = a^2 + c^2 - 2ac cos(B)
The parameters for this problem are given as follows:
a = 143, c = 70, B = 62.1º.
Hence the distance b is obtained as follows:
b² = 143² + 70² - 2 x 143 x 70 x cosine of 62.1 degrees
b² = 15981.
[tex]b = \sqrt{15981}[/tex]
b = 126.42 miles.
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Mr. Sanchez challenges his students to construct as many unique triangles as they can that have sides of 3 inches, 4 inches, and 8 inches. Which statement correctly describes how many triangles the students can construct with these side lengths?
A
They cannot construct any triangles with the given side lengths.
B
They can construct 1 unique triangle with the given side lengths.
C
They can construct 3 unique triangles with the given side lengths.
D
They can construct infinitely many unique triangles with the given side lengths.
Answer:
Step-by-step explanation:
The students cannot construct any triangles with the given side lengths because the sum of the two shorter sides of a triangle must always be greater than the longest side (i.e., the triangle inequality). However, in this case, 3 + 4 = 7, which is less than 8. Therefore, it is not possible to construct a triangle with sides of length 3, 4, and 8 inches.
So, the correct option is A - "They cannot construct any triangles with the given side lengths."
People, I need to figure out a question
Is the sun of 7/10 + 1/5 closer to 0, 1/2 or 1?
Answer:
1
Step-by-step explanation:
7+10+1/5
7/10 = 0.7
1/5 = 0.2
0.7+0.2=0.9
Therefore it would be closest to 1.
Answer: 1
Step-by-step explanation:
To find an estimate, you need to round your fractions. Let's start with 7/10. First let's look at the numerator, 7. 7 is a number greater than 5, so we'll round it to 10 and you keep your denominator. so now we have 10/10, or 1. Then round 1/5. 1/5 is lower than 5, so we'll round it to 0. Now, for the final step add them. 1 + 0 = 1, so 1 is the answer
Two coins are tossed. Assume that each event is equally likely to occur.
a) Use the counting principle to determine the number of sample points in the sample space.
b) Construct a tree diagram and list the sample space.
c) Determine the probability that no tails are tossed.
d) Determine the probability that exactly one tail is tossed.
e) Determine the probability that two tails are tossed.
f) Determine the probability that at least one tail is tossed.
Question content area bottom
Part 1
a) There is/are ______sample point(s) in the sample space.
a) There are 2 x 2 = 4 sample points in the sample space
How to solve
b) Tree Diagram
O D.\nH\nHe\nT\nH\nT\n
Sample space: D. HH, HT, TH, TT
c) P(no tails) = P(HH)
= 1/4
d) P(exactly one tail) = P(HT, TH)
= 2/4
= 1/2
e) P(2 tails) = P(TT)
= 1/4
f) P(at least one tail) = P(HT, TH, TT)
= 3/4
In mathematics, tree diagrams are often used in probability and statistics to show all the possible outcomes of an event. In computer science, they are used to represent the hierarchical structure of files and directories in a file system
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Casey is going to wear a gray sportscoat and is trying to decide what tie he should wear to work. In his closet, he has 29 ties, 15 of which he feels go well with the sport coat. If Casey selects one tie at random, determine the probability and the odds of the tie going well or not going well with the sport coat.
The probability of Casey selecting a tie that goes well with the sport coat is 0.517.
The probability of Casey selecting a tie that does not go well with the sport coat is 0.483
What are the probability and the odds of the tie going well or not going well with the sport coat?The probability of Casey selecting a tie that goes well with the sport coat is:
P(goes well) = 15/29
P(goes well) ≈ 0.517
The probability of Casey selecting a tie that does not go well with the sport coat is:
P(does not go well) = 1 - P(goes well)
P(does not go well) = 1 - 15/29 = 14/29
P(does not go well) ≈ 0.483
The odds in favor of the tie going well with the sport coat are:
P(goes well) : P(does not go well) = 15/29 : 14/29
P(goes well) : P(does not go well) = 15:14
The odds against the tie going well with the sport coat are:
P(does not go well) : P(goes well) = 14/29 : 15/29
P(does not go well) : P(goes well) = 14:15
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Every weekend, Camilla teaches ice skating lessons at a nearby ice rink. She earns $12 for a
30-minute lesson.
Complete the table.
Minutes taught
30
Money earned ($) 12
Graph the data from the table.
60
90 120
Next, using the matching x and y values for each row of the table, we can place a point for each row and connect it to the other points using a line.
what is line ?A line represents a one-dimensional straight figure that can go on forever in both directions in geometry. To separate it from a curved or an angle-filled line, it is frequently referred to as a "straight line." Two points on a line define the line, while every other position on the line may be discovered by tracing the line through the two defined points. A line can be made with a pencils or another non-thick tool, and it can have any width or depth. Shape and figures are described and analysed using lines, which are a basic building block of geometry.
given
Minutes Taught Dollars Earned (30, 12, 60, 24)
90 36
120 48
We may plot the minutes taught on the x-axis and the money made on the y-axis to graph the data from the table.
Next, using the matching x and y values for each row of the table, we can place a point for each row and connect it to the other points using a line.
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What's the difference between $4 and 36 cents
Answer:
364 cents or $3.64
Step-by-step explanation:
We can first convert $4 into cents. There are a 100 cents in $1, so there are 400 cents in $4. Now we can subtract.
400 - 36 = 364
Difference is 364 cents or $3.64
Make a rap about why triangular pyramids are the best shape. No cursing. It must be appropriate and at least 1 minute long.
The rap about why triangular pyramids are the best shape is given below.
Why Triangular Pyramids are the best shape lyricsVerse 1:
Listen up, y'all, I'm here to spit some truth
About a shape that's often overlooked, but it's the truth
It's the triangular pyramid, and let me tell you why
It's the best shape out there, and that's no lie
Chorus:
Triangular pyramids, they're the way to go
Strong and sturdy, they're the best, you know
With their pointed tips and angled sides
They're the perfect shape, no need to hide
Verse 2:
When it comes to architecture, they're the top choice
Their shape is so versatile, you can't deny its voice
From ancient pyramids to modern buildings tall
The triangular pyramid can withstand it all
Chorus:
Triangular pyramids, they're the way to go
Strong and sturdy, they're the best, you know
With their pointed tips and angled sides
They're the perfect shape, no need to hide
Verse 3:
And let's not forget their mathematical prowess
Their angles add up to 180, no need to guess
With their faces all congruent, they're a sight to see
The triangular pyramid, it's the shape for me
Chorus:
Triangular pyramids, they're the way to go
Strong and sturdy, they're the best, you know
With their pointed tips and angled sides
They're the perfect shape, no need to hide
Outro:
So there you have it, folks, the triangular pyramid
It's the best shape out there, there's no need to forbid
From its strength to its geometry
The triangular pyramid, it's the shape for me!
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In circle S with
m
∠
R
S
T
=
102
m∠RST=102 and
R
S
=
6
RS=6 units, find the length of arc RT. Round to the nearest hundredth.
In a circle, the measure of a central angle is equal to the measure of its intercepted arc. Since ∠RST is a central angle of circle S and its measure is 102 degrees, the measure of its intercepted arc ⌢RT is also 102 degrees.
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Since RS is a radius of circle S and its length is 6 units, the circumference of circle S is C = 2π * 6 = 12π units.
The length of an arc is proportional to its measure in degrees. Since the measure of ⌢RT is 102 degrees and the total measure of a circle is 360 degrees, the length of ⌢RT is (102/360) * 12π = 3.4π units.
Rounded to the nearest hundredth, this is approximately 10.68 units.
Need help with number 1!! Pleaseee
Answer:
Step-by-step explanation: find the circumference and then consider the shape (circle) after that get rid of options that don't make sense like 7.3 and 7.1, 8 for the radius might be too big leaving you with 7 (use a calculator if needed)
Prepare the journal entry to record Jevonte Company's issuance of 29,000 shares of its common stock assuming the shares have a
a. $3 par value and sell for $16 cash per share.
b. $3 stated value and sell for $16 cash per share.
View transaction list
Journal entry worksheet
<
2
Record the issuance of 29,000 shares of common stock assuming the shares
have a $3 par value and sell for $16 cash per share.
Note: Enter debits before credits.
Transaction
General Journal
Cash
Common stock, $3 par value
Paid-in capital in excess
Debit
Credit
The journal entry to record the transaction is given:
Account Debit Credit
Cash $464,000
Common Stock, $3 par value $87,000
Paid-in capital in excess of par $377,000
What is a journal entry?A journal entry is used to record a business transaction in the accounting records of a business.
A journal entry is usually recorded in the general ledger. Alternatively, it may be recorded in a subsidiary ledger that is then summarized and rolled forward into the general ledger
Assuming the shares have a $3 par value and sell for $16 cash per share:
Cash reeived from issuance of 29,000 common shares = 29,000 x $16 = $464,000
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An oil candle globe made of hand-blown glass has a diameter of 25.8 cm. What is the volume of the globe? Use 3.14 for .
globe meaning a sphere, and since it has a diameter of 25.8, that means its radius is half that, or 12.9
[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=12.9 \end{cases}\implies V=\cfrac{4\pi (12.9)^3}{3}\implies \stackrel{ using~\pi =3.14 }{V\approx 8987.47}[/tex]
Please help me with this question
Answer:
A
Step-by-step explanation:
based on summation, this is an integral from 1 to 6
answer choice A makes sense since plugging in K value gives appropriate riemann sum
HELP ME PLEASE!
Whoever answers right gets brainliest!
Therefore, the range of the relation shown is (1, 3, 4, 6, 7). Option C is the correct answer.
What is function?In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is associated with exactly one output. In other words, a function is a rule that assigns a unique output value to each input value. Functions are used to model relationships between variables in many areas of mathematics and other fields such as physics, engineering, economics, and computer science. They are used to describe various phenomena, such as the growth of populations, the trajectory of a projectile, or the behavior of financial markets. Functions are also important tools in calculus, where they are used to study rates of change and continuity, among other things.
Here,
The range of a relation refers to the set of all possible output values or y-values of the relation. Looking at the image reference, we can see that the y-values or the outputs are 1, 3, 4, 6, and 7.
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5. Complete the following table. (HINT: determine the reference angle and the quadrant of each angle.)
The given angles are 7π/4, 10π/3 & 510°.
Calculations for 7π/4(4th Quadarant)
sin(7π/4) = -1/√2
cos(7π/4) = 1/√2
tan(7π/4) = -1
cosec(7π/4) = -√2
cot(7π/4) = -1
sec(7π/4) = √2
Calculations for 10π/3(3rd Quadarant)
sin( 10π/3) = -√3/2
cos(10π/3) = -1/2
tan(10π/3) = √3
cosec(10π/3) = - 2/√3
cot(10π/3) = 1/√3
sec(10π/3) = -2
Calculations for 510°(2nd Quadarant)
sin( 510°) = 1/2
cos(510°) = -√3/2
tan(510°) = -1/√3
cosec(510°) = 2
cot(510°) = -√3
sec(510°) = -2/√3
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divide $300 in ratio 9 : 1
Answer:
$270:$30
Step-by-step explanation:
add up the ratios = 10
then do 300/10 = 30
so 1 ratio = 30
this means the ratio will be: $270:$30
Let me know if this helped
College Trig Question!!!!!!!!!!!!!!
The equation, for the simple harmonic motion of a particle moving uniformly is s ( t ) = A x cos (ωt).
How to find the equation ?An object undergoing simple harmonic motion follows a periodic oscillation in a straight line, resembling a sinusoidal curve. Likewise, when an object continuously traverses upon a circle with uniform motion, its projection along the diameter travels back and forth in a simple harmonic motion pattern.
Assuming that the particle commences at the highest point of the simple harmonic motion at time t = 0, either the sine or cosine function is utilized to derive the equation for the simple harmonic motion formula. Thus, let us employ the cosine function in this instance:
s ( t ) = A x cos (ωt)
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Solve for x. Round to the nearest tenth, if necessary
Using the tangent ratio, the value of x in the right triangle shown is calculated to the nearest tenth as: 2.6 units.
How to Find the Value of x Using the Tangent Ratio?The tangent ratio is part of the trigonometry ratios that is applied when solving a right triangle, and it is expressed as:
tan ∅ = length of the opposite side / length of the adjacent side.
We are given the following information from the image above:
Reference angle (∅) = 43 degrees
length of the opposite side = x
length of the adjacent side = 2.8
Plug in the values:
tan 43 = x/2.8
2.8 * tan 43 = x
x = 2.6 [to the nearest tenth]
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The estimated population of a certain city over time is given in the table below. Answer the questions below to determine what kind of function would best fit the data, linear or exponential.
Number of Years Since Last Census, x
1
2
3
4
Estimated Population, f(x)
49,372
58,207
66,998
75,798
function would best fit the data because as x increases, the y values change
. The
of this function is approximately
.
A linear function would best fit the data because as x increases, the y values change by an approximate constant. The rate of change of this function is approximately 8950 people a year.
How to determine that it is a linear functionTo determine which type of function best fits the data, we can analyze the difference in the y values (Estimated Population) as x increases.
Differences between consecutive y values:
58,207 - 49,372 = 8,835
66,998 - 58,207 = 8,791
75,798 - 66,998 = 8,800
The differences between consecutive y values are relatively constant as x increases. This suggests that a linear function would be more appropriate than an exponential function
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in the figure shown, the darker square is removed. Divide the remaining figure into two rectangles
The dimensions of each rectangle are x by (x- y) and y by (x - y); option A and D
The area of each rectangle is x² - 2xy + y² and x² - xy
The total area of the remaining figure is 2x² - 4xy + 2y²
This figure represents the difference of two squares in that x² - y² = (x + y)(x -y)
What is the are of each triangle?The area of each rectangle is:
x * (x- y) = x² -xy
and
y * (x - y) = xy - y²
The total area of the remaining figure is:
x² -xy + xy - y² = x² - y²
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What is the answer for this problem and tell me how it is correct.
Answer:
Step-by-step explanation:
D is the correct answer.
Answer:
D
Step-by-step explanation:
By reading the graph, place the art museum at location (5,5). Then check all the locations to see which statement is true.
A is not true because the art museum is located 4 units east and 1 unit north from the coliseum.
B is not true because the art museum is located 3 units east and 3 units north of the smith's tower.
C is not true because the art museum is located 1 unit east and 2 units north of the state capital.
This is why D is the correct answer.
In cell D7, enter a formula without using a function that multiples the Monthly_Payment (cell D6) by the Term_in_Months (cell D5), and then subtracts the Loan_Amount (cell B8) from the result to determine the total interest.
In cell D8, enter a formula without using a function that adds the Price (cell B6) to the Total_Interest (cell D7) to determine the total cost.
1. To find the interest we will use = (D6*D5) - B8, 2. To find the total cost we will use = B6 + D7.
Here we are given the financial information of a firm and are required to give an appropriate formula for total interest and total cost
1.
Here we need to multiply D6 and D7 and subtract B8 from the result. We cannot use any function. Hence we will simply write
= (D6*D5) - B8
The bracket is not necessary but can be put s an added satisfaction that the said formula would multiply the cells first and then only will the loan amount would be subtracted.
2.
Similarly, for cell D8, we need to go to the formula bar and write
= B6 + D7
This will add the cells up to give us the total cost.
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Complete Question
In cell D7, enter a formula without using a function that multiples the Monthly_Payment (cell D6) by the Term_in_Months (cell D5), and then subtracts the Loan_Amount (cell B8) from the result to determine the total interest.In cell D8, enter a formula without using a function that adds the Price (cell B6) to the Total_Interest (cell D7) to determine the total cost(Image Attached)
The table shows the home state of the 175 high school students who attended a tri-state debate tournament. The ratio of Illinois students to Michigan students was 6:5. How many students were from Indiana?
Let's start by setting up a proportion to represent the ratio of Illinois students to Michigan students:
Illinois students / Michigan students = 6/5
We can simplify this proportion by multiplying both sides by 5:
Illinois students = 6/5 * Michigan students
Next, we can use the information in the table to set up an equation that relates the number of Illinois students, Michigan students, and Indiana students:
Illinois students + Michigan students + Indiana students = 175
We can substitute the expression we obtained for the number of Illinois students into this equation:
6/5 * Michigan students + Michigan students + Indiana students = 175
Multiplying both sides by 5 to eliminate the fraction, we get:
6 * Michigan students + 5 * Michigan students + 5 * Indiana students = 875
Combining like terms, we get:
11 * Michigan students + 5 * Indiana students = 875
Now we can use the fact that the ratio of Illinois students to Michigan students is 6:5 to set up another equation:
Illinois students / Michigan students = 6/5
Substituting the values from the table, we get:
Illinois students / Michigan students = 24/20
Cross-multiplying, we get:
Illinois students * 20 = Michigan students * 24
Simplifying, we get:
Illinois students = 6/5 * Michigan students = 24/20 * Michigan students = 6/5 * 24 Michigan students = 28.8 Michigan students
Since the number of students must be a whole number, we can round 28.8 up to 29. This means that there were 29 Michigan students.
Substituting this into the equation we obtained earlier, we get:
11 * 29 + 5 * Indiana students = 875
Solving for Indiana students, we get:
5 * Indiana students = 875 - 11 * 29 = 546
Dividing both sides by 5, we get:
Indiana students = 546/5 = 109.2
Since the number of students must be a whole number, we can round 109.2 up to 110. This means that there were 110 Indiana students.
Therefore, the answer is 110 students from Indiana.
Need this answer please and show work
The value of the "trigonometric-expressions' are :
(a) tan(5π/2) is undefined,
(b) sec(315°) is √2.
Part(a) : The expression "tan(5π/2)" is undefined because the tangent function is undefined at odd multiples of π/2, which includes 5π/2.
Part(b) : To find the value of sec(315°), we use the identity: sec(θ) = 1/cos(θ),
First, we convert 315° to radians:
Which is : 315° = (7π/4) radians;
Next, we find the value of cos(7π/4):
⇒ cos(7π/4) = cos(π/4) = (√2)/2;
Finally, we substitute in the identity for sec(θ);
So, Sec(7π/4) = 1/cos(7π/4) = 1/[(√2)/2] = √2.
Therefore, value of sec(315°) is √2.
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The given question is incomplete, the complete question is
Find the value of the trigonometric expressions :
(a) tan(5π/2)
(b) sec(315°)