If Jake whittles little wooden figurines and begins to sell them. If the demand function for his figurines is given by D(q) = 80 - 1.25q and the supply function is S(q) = 0.75g. The equilibrium quantity is 40 units.
How to find the equilibrium quantity?Given the demand function D(q) = 80 - 1.25q and the supply function S(q) = 0.75q, we can find the equilibrium quantity by setting these two functions equal to each other and solving for q:
D(q) = S(q)
80 - 1.25q = 0.75q
Simplifying this equation, we get:
2q = 80
q = 40
Therefore, the equilibrium quantity is q = 40. At this quantity, the quantity demanded is:
D(q) = 80 - 1.25q = 80 - 1.25(40) = 30
And the quantity supplied is:
S(q) = 0.75q = 0.75(40) = 30
Thus, the equilibrium quantity of Jake's wooden figurines is 40 units.
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If the light is coming from the same position, the length of a person's shadow is proportional to their height. Adam and Cara are standing side-by-side, facing their shadows. Adam is 159 centimeters tall and casts a shadow 105 centimeters in height. If Cara is 140 centimeters tall, how many centimeters will she need to walk forward for the tip of her shadow to be directly in line with Adam's?
100 POINTS + BRAINLIEST
Find a number between 100 and 200 which is also equal to a square number
multiplied by a prime number.
Answer:
Numbers between 100 and 200 which are also equal to a square number multiplied by a prime number are:
108, 112, 116, 117, 124, 125, 128, 147, 148, 153, 162, 164, 171, 172, 175, 176, 180, 188, 192Step-by-step explanation:
A square number is a number that has been multiplied by itself.
For example, 25 is a square number as 5 × 5 = 25.
The square numbers between zero and 200 are:
4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196.A prime number is a whole number greater than 1 that cannot be made by multiplying other whole numbers (its only factors are 1 and itself).
Since the smallest square number is 4, and our final number needs to be between 100 and 200, we only need to list the primes numbers that are less than 50 as 4 × 50 = 200.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.Begin with the smallest prime number, 2. If we divide 100 and 200 by this prime number, we get 50 and 100. Therefore, to find a number between 100 and 200 that is equal to a square number multiplied by a prime number, the square number should be more than 50 and less than 100. Therefore:
64 × 2 = 12881 × 2 = 162The next smallest prime number is 3. If we divide 100 and 200 by 3 we get 33.33.. and 66.66... Therefore, the prime number 3 should be multiplied by a square number that is more than 33 and less than 67:
36 × 3 = 10849 × 3 = 14764 × 3 = 192The next prime number is 5. If we divide 100 and 200 by 5 we get 20 and 40. Therefore, the prime number 5 should be multiplied by a square number that is more than 20 and less than 40:
25 × 5 = 12536 × 5 = 180Continuing this way, all the numbers that are between 100 and 200, which are also equal to a square number multiplied by a prime number are:
64 × 2 = 12881 × 2 = 16236 × 3 = 10849 × 3 = 14764 × 3 = 19225 × 5 = 12536 × 5 = 18016 × 7 = 11225 × 7 = 17516 × 11 = 1769 × 13 = 1179 × 17 = 1539 × 19 = 1714 × 29 = 1164 × 31 = 1244 × 37 = 1484 × 41 = 1644 × 43 = 1724 × 47 = 188Number between 100 and 200 which is also equal to a square number multiplied by a prime number is 147.
Further Explanation:A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In simpler terms, a prime number is a number that can only be evenly divided by 1 and itself.
To find this number, I first looked for square numbers between 100 and 200. The square numbers within this range are 121 (11 squared) and 169 (13 squared).
I then checked if either of these square numbers could be multiplied by a prime number to equal a number between 100 and 200. After some calculation, I found that 169 cannot be multiplied by a prime number to give a number between 100 and 200. However, 121 can be multiplied by 2 to give 242, which is greater than 200.
Finally, I checked if there were any other square numbers I missed. I found that 7 squared is equal to 49, which when multiplied by 3 (a prime number) gives 147, a number between 100 and 200 that satisfies the problem.
Therefore, the number between 100 and 200 which is also equal to a square number multiplied by a prime number is 147.
I hope this helps!
I need help finding the regression equation pls!
Answer:
i did this in 8th grade. (I'm homeschooled)
Step-by-step explanation:
Heres the best i got
Solve the following. Find the unknown term of the proportion.
Problem:
If 3 pieces of shirts costs Php100. How much are you going to pay for 12 pieces of shirts?
Ps: kung di niyo alam yung sagot wag niyo kunin yung points :))
Answer:
Step-by-step explanation: 12 / 3 = 4, so php100 x 4 = Php400
Birthday Party!
Sandy and her twin brother Jason are having a birthday party, but... they haven't yet decided how many candy bars to buy.
and they haven't yet decided how many people to invite!
They made a chart to
write down all the
possible combinations
of people and candy
bars so they could
figure out how many people to invite
and how many candy bars to buy.
Across the top is the number of
people they are thinking about
inviting. On the left is the number of
candy bars they are thinking about
buying.
Help them fill out the chart!
Put the number of candy bars that
each person will get in the cell. Look
for patterns as you work to help you
fill the chart out more quickly!
What patterns do you see in the
chart?
How many candy bars will they buy?
1
2
3
4
5
6
7
8
9
10
1
How many people will they invite?
3
5 6
7
8
2
4
5.7 Apprentice Birthday Party Student
Unless otherwise noted, SFUSD Math Core Curriculum is licensed under the Creative Commons Attribution 40 International License
9 10
Based on the information we can infer that the number of candy bars they buy depends on the number of guests you have.
How to find the number of candy bars they are going to buy?To find the number of candy bars they are going to buy we need to look at the graph. In this case, if the maximum number of bars they are going to buy is 10 and the maximum number of people they are going to invite is 10, we can infer that 1 bar would correspond to each person.
Based on the above, we can infer that the relationship is directly proportional between the candy bars and the guests. In accordance with the above, the number of sweets depends on the number of guests.
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The average salary for a Queens College full professor is $85,900. If the average salaries is normally distributed with
standard deviation of $11,000, find the percentage of professors that make more than $75,000.
According to the question approximately 83.89% of professors make more than $75,000 calculated by forming the equation.
Explain equation?When the roots and solutions of two equations match, they are said to be equivalent. The same number, symbols, or expression must be added to or subtracted from both the equation's two sides to produce an equivalent equation. By multiplying or dividing both sides of an equation by a nonzero number, we can also obtain an analogous equation.
This issue can be resolved using the conventional normal distribution. First, we need to standardize the value of $75,000 using the formula:
z = (x - μ) / σ
where x is indeed the value we wish to standardise, is indeed the mean, and is the deviation.
z = (75,000 - 85,900) / 11,000
z = -0.99
Next, we look up the area to the right of z = -0.99 in the standard normal distribution table or by using a calculator. The area to the left of z = -0.99 is 0.1611, so the area to the right of z = -0.99 is:
1 - 0.1611 = 0.8389
Therefore, approximately 83.89% of professors make more than $75,000.
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5/6 plus negative 4/9 minus negative 2
Answer:
Step-by-step explanation:
5/9 + (-4/9) - (-2)
5/9 - 4/9 + 2
[tex]5-4+18/9[/tex]
19/9 or 2.1, 2 1/9
Simplify to create an equivalent expression.
−
4
(
−
11
+
4
n
)
−
3
(
−
2
n
+
9
)
Answer:
Step-by-step explanation:
To simplify this expression, we will distribute the -4 and -3 to the terms inside the parentheses:
-4(-11+4n) - 3(-2n+9)
= 44 - 16n + 6n - 27
= -16n - 17
Therefore, the simplified expression is -16n - 17.
Linear or non-linear?
What is the area of the composite figure?
Answer:
It is the area of combined shapes of one or more simple polygons and circles.
Can someone help
me?
Answer:
To find the real and imaginary parts of the complex number 26 = a + bi, we can use the fact that:
a + bi = 26
Taking the complex conjugate of both sides, we get:
a - bi = 26
Adding the two equations, we get:
2a = 52
Solving for a, we get:
a = 26
Substituting this value into one of the equations, we get:
26 + bi = 26
Therefore, b = 0.
Therefore, the real part of 26 is a = 26, and the imaginary part is b = 0.
Determine the product. Write your answer in scientific notation.
(15.4 × 102) · (2.8 × 10–4) = ?
A. 431.2 x 10^2
B. 43.12 x 10^-3
C. 4.312 x 10^-1
D. 431.2 x 10^-4
The product of (15.4 × 102) · (2.8 × 10–4) in scientific notation is written as 4.312 x 10⁻¹. Thus, option C is was correct.
How should a product be written in scientific notation?When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, the scientific notation for 650,000,000 is 6.5 108.
⇒ (15.4 × 10²) · (2.8 × 10⁻⁴)
= 15.4 × 2.8 × 10² × 10⁻⁴
= 43.12 × 10² × 10⁻⁴
= 4.312 × 10¹ × 10² × 10⁻⁴
= 4.312 × 10¹⁺²⁻⁴
= 4.312 × 10⁻¹
Thus, The product of (15.4 × 102) · (2.8 × 10–4) in scientific notation is written as 4.312 x 10⁻¹. Thus, option C is was correct.
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pls help quick. this was due a while ago. my math teacher doesnt teach and tells us to “read from the book.”
Answer:
183.3
Step-by-step explanation:
Since there were 1 angle and 2 sides, I used law of cosines
prove this question in the image please
The parallelogram ABCD's congruency can be proven using Side-Angle-Side (SAS) congruence theorem.
How to prove congruency?Prove that ΔABC ≅ ΔDCB using the Side-Angle-Side (SAS) congruence theorem.
Given that ABCD is a parallelogram, AB || CD and BC || AD. Therefore, ∠ABC ≅ ∠DCB and ∠ACB ≅ ∠DCA because they are corresponding angles.
AB ≅ CD and BC ≅ AD because opposite sides of a parallelogram are congruent.
Lastly, AC ≅ AC because it is a shared side between the two triangles.
Therefore, the following congruent parts:
∠ABC ≅ ∠DCB (by corresponding angles)
AB ≅ CD (by opposite sides)
BC ≅ AD (by opposite sides)
AC ≅ AC (shared side)
The SAS congruence theorem concludes that ΔABC ≅ ΔDCB.
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Image transcribed:
Prove ΔABC ≅ ΔDCB
find dy/dx y=e^x(e^-2x+7)
The chain rule is used when a function is composed of two or more functions, where one function is applied to the output of the other. In other words, it is used when a function is "nested" inside another function. Thus, option A is correct.
What is chain rule and the product rule of differentiation?We can solve this problem by applying the chain rule and the product rule of differentiation. Let's begin by simplifying the expression inside the parentheses:
[tex]y = ex (e^-2x + 7)[/tex]
Now, let's apply the product rule:
[tex]dy/dx = (ex)'(e^-2x + 7) + ex(e^-2x + 7)'[/tex]
Using the chain rule, we can find (ex)':
[tex](ex)' = ex[/tex]
And using the chain rule again, we can find [tex](e^-2x + 7)':[/tex]
[tex](e^-2x + 7)' = (-2e^-2x)[/tex]
Substituting these values back into the original equation, we get:
[tex]dy/dx = ex(e^-2x + 7) + ex(-2e^-2x)[/tex]
Simplifying, we get:
[tex]dy/dx = ex(e^-2x + 7 - 2e^-2x)[/tex]
[tex]dy/dx = ex(e^-2x - e^-2x + 7)[/tex]
[tex]dy/dx = ex(7)[/tex]
Therefore, the answer is A) 7.
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Quilt squares are cut on the diagonal to form triangular quilt pieces. The hypotenuse of the resulting triangles is 28 inches long. What is the side length of each piece?
A.14in
B. 14 √2in
C. 14 √3in
D.28 √2in
After cutting the squares, the length of each shorter side (and the side length of each triangular quilt piece) is approximately 14√2 inches i.e. B.
What are squares?
A square is a two-dimensional shape with four straight sides that are of equal length and four right angles (90-degree angles) at the corners. It is a special case of a rectangle, where all four sides are the same length. A square can also be thought of as a special type of rhombus, where the angles are all right angles.
Now,
Since the hypotenuse of each triangle is 28 inches long, we know that this is also the longest side of the right triangle formed by the two shorter sides of the triangle. Let's call one of the shorter sides x.
Using the Pythagorean Theorem, we can find the length of the other shorter side:
c²= a² + b²
28² = x² + x²
784 = 2x²
x² = 392
x = √(392)
x=14√2 in
Therefore, the length of each shorter side (and the side length of each triangular quilt piece) is approximately 14√2 inches (rounded to two decimal places).
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Find the interquartile range.
Answer:
3.7
Step-by-step explanation:
1.5, 2.2, 2.8, 3.4, 5, 5.6, 6.8, 7
Q1 = 2.2+2.8 = 5.0 divided 2 = 2.5
Q3 = 5.6+6.8 = 12.40 divided 2 = 6.2
IQR = 6.2 - 2.5 = 3.7
Please vote brainliest and rate if helpful
Angela, Breanna, Christine, Debbie, and Esther are in a club and they need to pick two people to go to a
meeting. They write each person’s name on equally sized pieces of paper, put them in a hat, and mix the
papers thoroughly. Find the probability model for this chance process and use it to determine the probability
that Angela gets to go to the meeting.
So the probability that Angela gets to go to the meeting is 2/5.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain. Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is an important concept in many fields, including mathematics, statistics, physics, and engineering, and is used to make predictions, analyze data, and make decisions under uncertainty.
Here,
There are a total of 5 people in the club, so there are 10 possible pairs of people that could be chosen to go to the meeting. Since each pair is equally likely to be chosen, the probability of any particular pair being chosen is 1/10.
To determine the probability that Angela gets to go to the meeting, we need to count the number of pairs that include Angela. There are 4 other people in the club, so there are 4 possible pairs that include Angela. Therefore, the probability that Angela gets to go to the meeting is:
P(Angela) = number of pairs that include Angela / total number of pairs
= 4 / 10
= 2 / 5
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Why is the second open interval on which the function is decreasing (0, infinity) and not (0, -infinity) if it’s going down? (Photo attached)
Therefore , the solution of the given problem of function comes out to be the function's behavior on that range because it is not specified for negative values of x.
What does the term function actually mean?The midterm exam will include questions on design, geometry, numbers, each division, as well as actual and hypothetical geographic places. A piece of work describes the connections between variable elements that cooperate to produce the same outcome. A utility is a structure made up of numerous unique parts that work together to create unique outcomes for each input.
Here,
Given that the function in the graph you supplied is undefinable for negative values of x, its domain is (0, infinity).
Therefore, referring to the function as declining on the interval is illogical. (0, -infinity).
As we travel from right to left on the interval, we can observe that the function's values are indeed decreasing. (0, infinity).
We refer to this interval as the function's declining one because of this.
On the interval, we could state that the function is decreasing.
(-infinity, 0). However, in this specific instance, we are unable to discuss the function's behavior on that range because it is not specified for negative values of x.
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[tex]\sqrt{2x} + 3 = 8[/tex]2 x + 3 = 8
Answer: x= 6241/2
Step-by-step explanation:
9x-7=-7 please answer quick
Answer:
x = 0
Step-by-step explanation:
9x - 7 = -7
Add 7 to both sides.
9x - 7 + 7 = -7 + 7
9x = 0
Divide both sides by 9.
9x/9 = 0/9
x = 0
Answer:
x=0
Step-by-step explanation:
A car is traveling at a speed of 80 miles per hour. What is the car's speed in kilometers per hour? How many kilometers will the car travel in 4 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
answer is
512
Step-by-step explanation:
1.6x80=128
128x4=512
PLEASE PLEASE HELP ME!!!!!!!!
The parallelogram H’I’J’K is a dilation of the parallelogram HIJK. What is the scale factor of the dilation?
Simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.
PLEASE LOOK AT PICTURE!!!!!!
Answer:
Horizontal Compress of 1/4.
Vertical compress of 1/4 as well.
Step-by-step explanation:
Looking at the graph the big Parallelogram HIJK gets becomes smaller parallelogram H'I'J'K'
I have counted the vertical and horizontal of the graph.
So the dilation is
Horizontal Compress of 1/4.
Vertical compress of 1/4.
Assume that the first term of a sequence is -3. Write the first four terms of the sequence if it is an arithmetic sequence with a common difference of -1/3.
Answer:
The first term of the sequence is -3 and the common difference is -1/3. Therefore, the second term of the sequence can be found by adding the common difference to the first term:
second term = first term + common difference
second term = -3 + (-1/3)
second term = -10/3
Similarly, we can find the third term by adding the common difference to the second term:
third term = second term + common difference
third term = -10/3 + (-1/3)
third term = -11/3
And we can find the fourth term by adding the common difference to the third term:
fourth term = third term + common difference
fourth term = -11/3 + (-1/3)
fourth term = -4
Therefore, the first four terms of the sequence are -3, -10/3, -11/3, and -4.
-4(X-1)+2 which of the following is equivalent to the expression
Answer:
-2 ( 2x - 3 )
Step-by-step explanation:
We know that,
( + ) × ( + ) = ( + )
( - ) × ( - ) = ( - )
( + ) × ( - ) = ( - )
Accordingly,
-4 ( x - 1 ) + 2
First, solve the brackets. That is, multiply each term inside the brackets by -4.
- 4x + 4 + 2
Combine like terms.
- 4x + 6
You can take the common factor out of the brackets.
-2 ( 2x - 3 )
What is an equation for the linear relationship in slope-intercept form?
A. y=2x+3
B. y=12x+3
C. y=12x−3
D. y=−12x−3
A: y=2x+3. This is an equation for the linear relationship in slope-intercept form. The equation states that the value of y is equal to the slope of the line, 2, multiplied by the value of x, plus 3.
What is slope?Slope is a measure of the steepness of a line. It is the ratio between the vertical change in a line (change in y-values) over the horizontal change in the same line (change in x-values). It is also referred to as the rate of change, as it is a measure of how quickly the value of y changes with respect to the x-value.
This equation is used to describe a straight line that has a constant rate of change between two variables. This equation can be used to determine the slope, y-intercept, and x-intercept of a line.
The slope, which is the coefficient of x in the equation (2 in this case), is the rate at which y changes with respect to x. It is the rise over run, or the change in y over the change in x. The y-intercept is the value of y when x is equal to 0 (in this case, it is 3). The x-intercept is the value of x when y is equal to 0 (in this case, it is -3/2).
This equation is often used to represent a linear relationship between two variables, such as the amount of money a person earns in relation to the number of hours they work.
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If sin a = -1/4 and π < a <3pi/2 and cos b= 5/9 and 0 < b < pi/2, find the exact value of the following. Show all your work and simplify your answers.
sin(a + B) =
Answer:
Step-by-step explanation:
(reposting because the one person that helped gotten their comment deleted so i couldnt see answer) PLEASE HELP ASAP WITH THIS
Answer:
64, 69, 88, 88, 91, 92, 93, 95, 97, 97, 100
Median= 92
Mode= 88, 97
Mean= 88.55
Range= 36
Quartile 1= 88
Quartile 2= 92
Quartile 3= 97
Interquartile range= 9
Minimum= 64
Maximum= 100
Not sure if this helped but I hope it did
5. Find the volume of the cylinder. Leave your
answer in terms of t.
8 cm.
8 cm.
The volume of the cylinder in terms of π is 128π centimetres³.
How to find the volume of a cylinder?The cylinder below has a height of 8 centimetres and a diameter of 8 centimetres. Therefore, the volume of the cylinder can be found as follows:
volume of the cylinder = πr²h
where
r = radiush = height of the cylinderTherefore,
r = 8 / 2 = 4 centimetres
h = 8 centimetres
volume of the cylinder = π × 4² × 8
volume of the cylinder = 128π centimetres³
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Write a linear equation in y=mx+b form to represent the scenario.Todd has $450 in his savings. He withdraws $10 per week.
The linear equation in y=mx+b form that represents this scenario is:
y = -10x + 450.
What is a linear equation?
A linear equation is a mathematical equation in which the highest power of the variable(s) is one.
ax + b = 0
or
y = mx + b
where a, b, and m are constants and x and y are variables. In the first form, x is a variable and a and b are constants. In the second form, x and y are variables, m is the slope of the line, and b is the y-intercept.
Let x be the number of weeks that have passed since Todd started withdrawing money from his savings account. Initially, Todd had $450 in his savings, so the amount of money he has left after x weeks is:
450 - 10x
The rate of change of the amount of money Todd has with respect to time is -10, since he is withdrawing $10 per week. Therefore, the slope of the line that represents this situation is -10.
The y-intercept represents the initial amount of money Todd had in his savings, which is $450. Therefore, the linear equation in y=mx+b form that represents this scenario is:
y = -10x + 450
where y is the amount of money Todd has in his savings after x weeks.
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