Answer:
4x² + 24x + 35
Step-by-step explanation:
Total area = (7 + 2x)(5 + 2x)
= 35 + 10x + 14x + 4x²
= 4x² + 24x + 35
Please help!!!
4. Graph the quadratic y=x²-2x-5 below
The vertex of the function is -6.
The domain of the function is {real numbers}.
The range of the function is y ≥ -6.
What are the domain and range of the function?The range and domain of the function is calculated as follows;
y = x² - 2x - 5
From the graph of the function, the range of the function includes y values;
range = y ≥ -6
From the graph of the function, the domain of the function includes x values;
domain = real numbers.
The vertex of the graph is -6.
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Triangle G Y K is shown. Angle G K Y is a right angle. Angle K G Y is 60 degrees and angle G Y K is 30 degrees. The length of G K is 27.
Given right triangle GYK, what is the value of tan(G)?
One-half
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction
StartRoot 3 EndRoot
The value of tanG is √3
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
The value of KY
Tan 30 = 27/KY
1/√3 = 27/KY
KY = 27√3
Tan G = 27√3/27
tanG = √3
therefore the value of tanG is √3
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A builder is creating a scale drawing of a plot of land as shown. The original plot of land is 335 meters wide. The drawing uses a scale factor of 1500.
Find the missing side length of the original plot of land in meters and the missing side length of the scale drawing in centimeters.
Original plot of land's length:
m
Scale drawing width:
The calculated width of the scale drawing is 0.67 cm and the missing side length is undefined
Finding the missing side length in the original plotWe have the following statements from the question
The width of the original plot is 335 metersThe scale factor of the drawing is 1/500.The above statements means that the width of the scale is
Scale width = 335 cm * 1/500
When the products are evaluated, we have the following
Scale width = 0.67 cm
This means that the width of the scale drawing is 0.67 cm
Also, the missing side length of the original plot of land in meters cannot be calculated
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Evaluate the integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb into C as much as possible.) / 25x2 + 46x + 13 dx = +4in(x + 1) + 21 In(x - 1)+C x+1 incorrect
The correct way to evaluate the integral of (25x² + 46x + 13)dx is:
∫(25x² + 46x + 13)dx = 4ln|x + 1| + 21ln|x - 1| + C
Here, ln represents the natural logarithm. The arbitrary constant, denoted by C, represents any constant value that could be added to the antiderivative without changing its derivative.
To evaluate the given integral, we will first rewrite it using the correct mathematical notation:
∫(25x² + 46x + 13) dx
Now, we will use integration techniques to find the antiderivative. In this case, we can apply the power rule and linearity of the integral:
∫(25x²) dx + ∫(46x) dx + ∫13 dx
Now we will evaluate each integral separately:
(25/3)x³ + (46/2)x² + 13x + C
Now, we can simplify the expression:
(25/3)x³ + 23x² + 13x + C
So the evaluated integral is:
(25/3)x³ + 23x² + 13x + C
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HELP match each one with either 1-4
Answer:
(4),(3),(1),(2),(2),(1)
Step-by-step explanation:
Mnemonic to memorize trigonometric ratios: SOH CAH TOA
(S=O/H C=A/H T=O/A)
Sine, Cosine, Tangent, Opposite to x, Adjacent to x, Hypotenuse
Cosecant = 1/Sine, Secant = 1/Cosine, Cotangent = 1/Tangent
46 inches = 3 ft 10 inches? is it true please give me an explanation
Answer: yes
Step-by-step explanation:
1 ft = 12 in so 3ft = 36 in
36in + 10in = 46in
Molly's cafe has regular coffee and decaffeinated coffee. this morning, the cafe served 30 coffees in all, 40% of which were regular. how many regular coffees did the cafe serve?
The cafe served 12 regular coffees.
Out of the 30 coffees served at Molly's cafe this morning, 40% were regular coffee. To determine the number of regular coffees, we can calculate 40% of 30.
To find the value,
Step 1: Convert the percentage to a decimal by dividing it by 100. So, 40% = 40/100 = 0.4.
Step 2: Multiply the total number of coffees served by the decimal. So, 30 * 0.4 = 12.
Hence, the cafe served 12 regular coffees. The remaining 60% (or 18 coffees) would be decaffeinated. It is important to note that percentages represent proportions or fractions of a whole. In this case, 40% indicates that 40 out of 100 parts (or 40/100) are regular coffees. By applying this proportion to the total number of coffees served (30), we can determine the specific quantity. This method can be used in various scenarios involving percentages to find a portion of a whole. Therefore, Molly's cafe served 12 regular coffees and 18 decaffeinated coffees, making a total of 30 coffees.
Your answer: Molly's cafe served 12 regular coffees this morning.
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Center: (2, 8) radius: 3
What is the equation of a circle with the center and radius given?
Henry earned $850 over the summer working odd jobs. he wants to put his money into a savings account for when he is ready to buy a car. his bank offers a simple interest account at 5%, how much interest will henry have earned after 4 years?
Answer:
We can use the formula for simple interest to calculate the interest earned by Henry:
Simple Interest = (Principal * Rate * Time)
where,
Principal = $850 (initial amount)
Rate = 5% per year (as given)
Time = 4 years (as given)
Substituting the values, we get:
Simple Interest = (850 * 0.05 * 4) = $170
Therefore, Henry will have earned $170 in interest after 4 years of keeping his money in the savings account.
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Solve problems 6,9, and 11 in the interval [0 pi, 2 pi]. Show all work, drawing diagrams as necessary.
The solutions to each trigonometric equation are:
Case 6: x = 50.768° (0.282π) or x = 129.232° (0.718π) or x = 230.768° (1.282π) or x = 309.232° (1.718π)
Case 9: x = 41.810° (0.232π) or x = 138.190° (0.768π) or x = 199.471° (1.108π) or x = 340.529° (1.892π)
Case 11: x = 208.164° (1.156π) or x = 331.836° (1.844π)
How to solve quadratic-like trigonometric equations
In this problem we find four cases of quadratic-like trigonometric equations, whose solutions must be found by means of algebra properties and trigonometric formulas. Now we proceed to solve for each case:
Case 6
cos² x + 3 / 5 = 1
cos² x = 2 / 5
cos x = ± √(2 / 5)
x = 50.768° (0.282π) or x = 129.232° (0.718π) or x = 230.768° (1.282π) or x = 309.232° (1.718π)
Case 9
9 · sin² x - 3 · sin x - 2 = 0
sin x = 2 / 3 or sin x = - 1 / 3
x = 41.810° (0.232π) or x = 138.190° (0.768π) or x = 199.471° (1.108π) or x = 340.529° (1.892π)
Case 11
sin² x - 8 · sin x - 4 = 0
sin x = - 0.472
x = 208.164° (1.156π) or x = 331.836° (1.844π)
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Stephanie throws a paper airplane off the roof of her school. Her classmates measure the plane’s height, in feet, after each second. The table shows some of her data.
T= 0, 1, 2, 3, 4
h(t)= 200, 208, 212, 212, 208
Find the equation for h(t), and use it to determine how long it will take the plane to hit the ground. Round to the nearest hundredth
The paper airplane will not hit the ground within the given time frame.
To find the equation for h( t), we need to find the rate of change or the pitch of the function. We can do this by chancing the difference in height and time for any two points on the line. Let's choose the first two points,( 0,200) and( 1,208).
pitch = ( change in height)/( change in time)
pitch = ( 208- 200)/( 1- 0) = 8
So, the equation for h( t) can be written in pitch- intercept form as h( t) = 8t b
To find the value of b, we can use any of the given points.
Let's use( 0,200) 200 = 8( 0) b b = 200
So, the equation for h( t) is h( t) = 8t 200
To find how long it'll take the aeroplane to hit the ground, we need to find when h( t) = 0,
since that would mean the height is 0 bases or the ground position. 0 = 8t 200 working for t,
we get t = -25
Since time cannot be negative the paper airplane will not hit the ground within the given time frame.
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Harold, Rhonda, and Brad added water to beakers in science class. The line plot shows the amount of water, in cups, that they added to each of 14 beakers.
In the given line plot, the data represents the amount of water, in cups, that Harold, Rhonda, and Brad added to each of 14 beakers in their science class.
A line plot is a way to represent data that involves marking a number line for each data point and placing an “X” above the number that represents the value of that data point.
The line plot shows that most of the beakers were filled with either 1 or 2 cups of water. Specifically, there are 5 beakers with 1 cup of water and 6 beakers with 2 cups of water. There are also 2 beakers with 3 cups of water and 1 beaker with 4 cups of water.
The line plot provides a visual representation of the data that allows the viewer to quickly understand the distribution of the data. By seeing that most of the data is clustered around 1 and 2 cups of water, one can infer that the students were likely instructed to add a specific amount of water to each beaker. However, the presence of a few outliers, such as the beaker with 4 cups of water, suggests that some of the students may have made errors in their measurements or not followed the instructions closely.
Overall, the line plot provides a quick and easy way to visualize the distribution of the data and identify any outliers or patterns in the data. It is a useful tool for representing small to medium-sized datasets and is commonly used in education, research, and data analysis.
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Answer:
if this is study island than the answer is:
All of the beakers with more than of a cup of water added to them were filled by Harold. Harold added a total of
4
cup(s) of water to his beakers.
All of the beakers with exactly of a cup of water added to them were filled by Rhonda. Rhonda added a total of
15/8 or 1 7/8
cup(s) of water to her beakers.
Brad filled the rest of the beakers. Brad added a total of
13/8 or 1 5/8
cup(s) of water to his beakers.
Step-by-step explanation:
TEXT ANSWER
Use the multiplication rule to simplify:
b7 . b²
Tip: When writing math questions, the coefficient would go in front of variables: 7b*[tex]b^2[/tex]
Anyways, in this case, since we cannot mutiply 7 by b, the 7 will stay put
But.... we can mutiply b by b
[tex]b^2[/tex][tex]*b[/tex]=b^3
Tip: B's with no exponent has an exponent with one
Questions?
So,7 will stay put and b and b^2 will simply to b^3
[tex]7b^3[/tex]=Answer
The equation m = 1. 4p represents the mass, m, in grams, of
p polished stones.
We know that the total mass of 5 polished stones would be 7 grams according to this equation
Sure! The equation m = 1.4p represents the mass, m, in grams, of p polished stones.
This means that if you know the number of polished stones, p, you can use this equation to calculate their total mass, m, in grams. For example, if you have 5 polished stones, you can plug in p = 5 and solve for m: m = 1.4 x 5 = 7 grams.
So the total mass of 5 polished stones would be 7 grams according to this equation.
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Based on the equation, the number of grams which the mass increase for every 7 polished stones is: D. 9.8 g.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.Based on the information provided above, a linear equation that models the mass in grams is given by;
y = mx + c
m = 1.4p
By substituting the given parameter (x = 7 polished stones), we have the following:
m = 1.4(7)
m = 9.8 g
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Ariel is filling a giant beach ball with air. The radius of the beach ball is 30 cm. What is the volume of air that the beach ball will hold? Either enter an exact answer in terms of Pi.
The volume of air that the beach ball will hold is 36000π cubic cm
What is the volume of air that the beach ball will holdFrom the question, we have the following parameters that can be used in our computation:
The radius of the beach ball is 30 cm.
This means that
r = 30
The volume of air that the beach ball will hold is calculated as
V = 4/3πr³
Substitute the known values in the above equation, so, we have the following representation
V = 4/3π * 30³
Evaluate
V = 36000π
Hence, the volume of air that the beach ball will hold is 36000π cubic cm
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a city maintains a database of all traffic tickets that were issued over the past ten years. the tickets are divided into the following two categories. moving violations nonmoving violations the data recorded for each ticket include only the following information. the month and year in which the ticket was issued the category of the ticket which of the following questions cannot be answered using only the information in the database? responses have the total number of traffic tickets per year increased each year over the past ten years? have the total number of traffic tickets per year increased each year over the past ten years? in the past ten years, were nonmoving violations more likely to occur on a weekend than on a weekday? in the past ten years, were nonmoving violations more likely to occur on a weekend than on a weekday? in the past ten years, were there any months when moving violations occurred more often than nonmoving violations? in the past ten years, were there any months when moving violations occurred more often than nonmoving violations? in how many of the past ten years were there more than one million moving violations?
The statement about the chances of occurrence of nonmoving violations more on a weekend than on a weekday in past ten years is cannot be answered using only the information in the database. So, option(b) is provide the right answer.
Database: The database is a large collection of data and it is used to store and retrieve the accordingly. It has an organization of a certain amount of data that needs and it contains. We have a database of all traffic tickets that were issued over the past ten years in a city. The informations including are
the tickets are divided into two categories. 1) moving violations2) nonmoving violations
the month and year in which the ticket was issued the category of the ticket.We have to recongise the statement which is not answering by the above informations in database. First statement is can be answerable, because we have data of year in which tickets are issued. Similarly, statements third and fourth related to data of tickets issued in month and year in past ten years. So, both are answerable statements. Therefore, the second statement
is cannot be answerable here.
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Complete question:
a city maintains a database of all traffic tickets that were issued over the past ten years. the tickets are divided into the following two categories. moving violations nonmoving violations the data recorded for each ticket include only the following information. the month and year in which the ticket was issued the category of the ticket which of the following questions cannot be answered using only the information in the database? responses
a) have the total number of traffic tickets per year increased each year over the past ten years?
b) in the past ten years, were nonmoving violations more likely to occur on a weekend than on a weekday?
c) in the past ten years, were there any months when moving violations occurred more often than nonmoving violations?
d) in how many of the past ten years were there more than one million moving violations?
3. 07 Quiz: Combine Functions Nearpod i H George has opened a new store and he is monitoring its success closely. He has found that this store's revenue each month can be modeled by r(x) = x2 + 5x + 14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by c(x) = x2 - 4x + 5 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars. What does (r - c)(5) mean about George's new store? -O The new store will sell 900 items in its fifth month in business.
George's new store will have a profit of $5,400 in its fifth month in business.
We are given two functions: r(x) = x^2 + 5x + 14 for revenue, and c(x) = x^2 - 4x + 5 for expenses. We are asked to find the meaning of (r - c)(5).
Step 1: Subtract c(x) from r(x) to find (r - c)(x)
(r - c)(x) = r(x) - c(x) = (x^2 + 5x + 14) - (x^2 - 4x + 5)
Step 2: Simplify the expression
(r - c)(x) = x^2 + 5x + 14 - x^2 + 4x - 5 = 9x + 9
Step 3: Evaluate (r - c)(5)
(r - c)(5) = 9(5) + 9 = 45 + 9 = 54
The value (r - c)(5) = 54 represents the difference between the revenue and expenses in the store's 5th month of operation, measured in hundreds of dollars. In other words, George's new store will have a profit of $5,400 in its fifth month in business.
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11. Consider the image shown. What is the measure of angle DEB?
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The supplementary angles of the given angles are 154 degrees, 136 degrees, 135 degrees, 44 degrees, 45 degrees, and 26 degrees, respectively.
Supplementary Angles of Given Angles
Supplementary angles are pairs of angles that add up to 180 degrees. To find the supplementary angle of each given angle, we simply subtract the angle from 180 degrees.
Therefore, the supplementary angles of the given angles are:
The supplementary angle of 26 degrees is 154 degrees (180 - 26 = 154).
The supplementary angle of 44 degrees is 136 degrees (180 - 44 = 136).
The supplementary angle of 45 degrees is 135 degrees (180 - 45 = 135).
The supplementary angle of 136 degrees is 44 degrees (180 - 136 = 44).
The supplementary angle of 135 degrees is 45 degrees (180 - 135 = 45).
The supplementary angle of 154 degrees is 26 degrees (180 - 154 = 26).
Therefore, the supplementary angles of the given angles are 154 degrees, 136 degrees, 135 degrees, 44 degrees, 45 degrees, and 26 degrees, respectively.
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Find X and then find JL
The value of x is calculated as x = 3, while the length of segment JL is calculated as 18 units.
How to Find the Value of x in the Figure Given?Create an equation based on the fact that the diagonals of the shape shown bisects each other to form equal segments such as:
JN = LN
Plug in the values to find x:
15 - 2x = 4x - 3
Combine like terms:
15 + 3 = 4x + 2x
18 = 6x
18/6 = x
x = 3
Length of JL = 15 - 2x + 4x - 3 = 12 + 2x
Plug in the value of x:
Length of JL = 12 + 2(3) = 18 units
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What is the measure of ∠SQR?
the ∠sqr is 4y= 4*29=116° we can get this answer with supplementary angle fact and sum of angle in triangle is 180 degree
what is supplementary angle ?
In geometry, two angles are called supplementary angles if their sum is equal to 180 degrees. In other words, if angle A and angle B are supplementary, Supplementary angles are commonly found in many geometric shapes, such as triangles and quadrilaterals, as well as in other applications of geometry. When two angles are supplementary, they form a straight line or a straight angle, which is an angle that measures exactly 180 degrees. For example, if one angle of a triangle measures 80 degrees, then the other two angles are supplementary and together measure 100 degrees (180 degrees - 80 degrees).
In the given question,
with the fact of complimentary angles we can write as follows
angle trq+ angle qrs =180
angle qrs=180-145=35 degree
so in triangle we have sum of all angle is 180 degree so we can write as follows
∠r+∠q+∠s=180
35+4y+y=180
5y=180-35
y=145/5
y=29 degree
so the ∠sqr is 4y= 4*29=116°
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Which expressions represent the length of side MN?
Choose 2 answers:
A. 4 • sin (65)
B. 1. 9 • cos (65)
C. 4/sin (65)
D. 1. 9/cos (65)
PLEASE HELP!!
Expressions A and B represent the length of side MN.
How can the length of side MN be expressed?The two expressions that represent the length of side MN are A) 4•sin(65) and B) 1.9•cos(65). The length of side MN can be found using the trigonometric ratios of sine and cosine in a right triangle.
The angle of 65 degrees is opposite to side MN and the hypotenuse of the triangle is given as 4 units. Using the sine ratio, we can find the length of MN as 4•sin(65). Similarly, using the cosine ratio, we can find the length of MN as 1.9•cos(65).
Therefore, expressions A and B both represent the length of side MN, and they have been obtained by using different trigonometric ratios.
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ETA 4
Answer the following:
Myla bought an item P2,500. She decided to sell it wil 2% markup. How much will Myla’s selling price be?
Joan sold her old iphone for P5000 at 8% markdown rate. Find the markdown and the original cost of the phone.
A student assistant bought an item for P520 but later decided to sell it at P550. What is the markup?
Mother organize a garage sale and earned P120 on one item at 60% markdown. How much did mother buy the item?
The cost of a t-sirt from the manufacturer is P400. If loan wants a 30% markup based on the selling price, how much will her selling price be?
1. Myla bought an item for P2,500 and decided to sell it with a 2% markup. The selling price will be P2,500 + (2% of P2,500) = P2,500 + P50 = P2,550.
2. Joan sold her old iPhone for P5,000 at an 8% markdown rate. To find the markdown and the original cost, we first calculate the markdown: P5,000 = 92% of original price. So, the original price was P5,000 ÷ 0.92 ≈ P5,434.78. The markdown is P5,434.78 - P5,000 = P434.78.
3. The student assistant bought an item for P520 and sold it for P550. The markup is P550 - P520 = P30.
4. Mother earned P120 on an item at a 60% markdown. Let X be the original price, then X * 60% = P120. X = P120 ÷ 0.60 = P200. So, the mother bought the item for P200.
5. The cost of a t-shirt from the manufacturer is P400. If Loan wants a 30% markup based on the selling price, we'll let X be the selling price, then X - 30% of X = P400. So, 0.7X = P400. X = P400 ÷ 0.7 ≈ P571.43. Loan's selling price will be P571.43.
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Find the ordered pair (s,t) that satisfies the system
s/2+5/t=3
3t-6s=9
The ordered pair (s,t) that satisfies the system are (1/2,4) and (1,5).
We can use the second equation to solve for one of the variables in terms of the other. Let's solve for t:
3t - 6s = 9
3t = 6s + 9
t = (2s + 3)
Now we can substitute this expression for t into the first equation and solve for s:
s/2 + 5/t = 3
s/2 + 5/(2s + 3) = 3
Multiplying both sides by the denominator (2s + 3) gives:
s(2s + 3)/2 + 5 = 3(2s + 3)
Simplifying and collecting like terms yields:
2s^2 + 3s + 10 = 6s + 9
2s^2 - 3s + 1 = 0
This quadratic equation can be factored as:
(2s - 1)(s - 1) = 0
So s = 1/2 or s = 1.
Now we can substitute these values for s into the equation we derived for t:
If s=1/2 then t=2(1/2)+3=4
If s=1 then t=2(1)+3=5
Therefore, the ordered pairs that satisfy the system are (1/2,4) and (1,5).
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I need help with this question.
Answer: The answer is (C
Step-by-step explanation:
Or
Camille has a can of soup in the pantry. The circular lid has a radius of 3 inches. What is the lid's area?
Use 3. 14 for
The lid's area can be calculated using the formula for the area of a circle, which is A = πr^2, where A is the area and r is the radius.
So, for Camille's can of soup, the lid's area would be:
A = 3.14 x (3 inches)^2
A = 3.14 x 9 square inches
A = 28.26 square inches
Therefore, the lid's area is 28.26 square inches.
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Which graphs represent functions?
4
←
4
•
4
4 -2
++
Graph A
4
2
2
2
4
4
2 4
Graph C
X
-4
-2
4
-2
2
-2-
4
Graph B
у
4-
2
-2
Graph D
4
4
A survey found that the relationship between the years of education a person has and that person's yearly income in his or her first job after completing schooling can be modeled by the equation y - 1200x
7000, where x is the number of years of education and y is the yearly income. According to the model, how much does 1 year of education add to a person's yearly incomo?
А $1200
B
$5800
$7000
D
$8200
Answer:
The equation provided is y = 1200x + 7000, where y is the yearly income and x is the number of years of education.
To determine how much 1 year of education adds to a person's yearly income, we need to find the change in y when x increases by 1.
Let's plug in x and x+1 into the equation to find the corresponding yearly incomes:
When x = 1, y = 1200(1) + 7000 = $8200
When x = 2, y = 1200(2) + 7000 = $9400
The difference between these two yearly incomes is:
9400 - 8200 = $1200
Therefore, 1 year of education adds $1200 to a person's yearly income according to the model.
The answer is (A) $1200.
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Select the statement that best describes the expression 4+3x
A. 4 plus 3plus x
B. The sum of 4 and 3
C. The product of 4 and 3x
D. 4 plus 3 times x
The correct option is D, the statement that best describes the expression 4+3x means "4 plus 3 times x".
An expression is a combination of numbers, symbols, and/or variables that represents a mathematical or logical statement. It can be as simple as a single number or letter, or as complex as a series of operations that involve multiple variables and functions. Expressions can be used to represent equations, inequalities, functions, and other mathematical concepts. They can be evaluated to produce a numerical value or a boolean value (true or false) depending on the values of the variables involved.
Expressions are used to represent calculations or logical conditions. They can be used to assign values to variables, manipulate data, and control the flow of a program. expressions are a fundamental concept in both mathematics and computer science, and play a critical role in solving problems and building complex systems.
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Help me— My brain goes brrr in this question word problem thing ; - ;
A table tennis ball has a radius of 0. 04m. Estimate how many table tennis balls you could fit into the coin building! [search up what it is—]
( Width: 20m | height: 110m )
- How did you calculate your estimate?
- Explain how accurate you think your prediction is?
( Show Work. )
Number of balls ≈ [tex]1.03 * 10^9[/tex]
To calculate how many table tennis balls can fit into the coin building, we need to first figure out the volume of the building and the volume of the table tennis ball.
Then, we can divide the volume of the building by the volume of the ball to get an estimate of the number of balls that can fit inside.
The volume of a table tennis ball can be calculated using the formula for the volume of a sphere, which is:
V = (4/3)πr³
where V is the volume, π is pi (approximately 3.14), and r is the radius of the ball. In this case, the radius is given as 0.04m, so we can plug that in and get:
V = (4/3) x 3.14 x 0.04³
[tex]V =2.14 * 10^{-5} m^3[/tex]
Next, we need to find the volume of the coin building. The building has a width of 20m and a height of 110m, but we don't know its depth.
Let's assume that the building is a rectangular prism with a depth of 10m. Then, we can calculate its volume using the formula:
V = l x w x h
where l is the length, w is the width, and h is the height. Plugging in the given values, we get:
V = 20 x 10 x 110
V = 22000 m³
Now, we can divide the volume of the building by the volume of the ball to get an estimate of how many balls can fit inside:
Number of balls ≈ [tex]V_building / V_ball[/tex]
Number of balls ≈ 22000 / 2.14 x [tex]10^-5[/tex]
Number of balls ≈ [tex]1.03 * 10^9[/tex]
So we can estimate that approximately 1.03 billion table tennis balls can fit into the coin building.
As for the accuracy of this prediction, it's important to keep in mind that we made some assumptions and estimations in our calculations.
For example, we assumed that the building is a rectangular prism with a depth of 10m, which may not be completely accurate.
Additionally, we rounded some of our values and used approximations for pi.
Therefore, our estimate should be considered as a rough approximation rather than an exact calculation. Nonetheless, it gives us an idea of the scale of the building and how many objects it can hold.
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Find the minimum value of the average cost for the given cost function on the given intervals C(x)=x3 + 36x +432 (a) 1 sxs 10 (b) 10 5 x 20 (a) The minimum value of the average cost over the interval 15%$ 10 is N. (Round to the nearest tenth as needed. Do not include the $ symbol in your answer)
The minimum value of the average cost over the interval (1, 10).To find the minimum value of the average cost, we first need to find the average cost function.
The average cost is given by:AC(x) = C(x) / x
Substituting the given cost function, we get:
AC(x) = (x^3 + 36x + 432) / x
Simplifying this expression, we get:
AC(x) = x^2 + 36 + 432/x
Now, we need to find the minimum value of this function on the given intervals. To do this, we take the derivative of the function and set it equal to zero:
AC'(x) = [tex]2x - 432/x^2[/tex] = 0
Solving for x, we get:
x = [tex](216)^{(1/3)[/tex] ≈ 6.89
This critical point lies within the interval (1, 10), so we need to check the endpoints as well as this critical point to determine the minimum value of the average cost.
Calculating the values of the average cost at these three points, we get:
AC(1) = 469
AC(6.89) ≈ 51.9
AC(10) = 78.4
Therefore, the minimum value of the average cost over the interval (1, 10) is approximately $51.9. Note that this value is rounded to the nearest tenth as requested.
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