They already cover 20 mi and every hour they advance 50mi, so if we call f(x) as the distance and x as the time in hours the function will be:
\(f(x)=50x+20\)The mimimun value for x has to be 0 because when x = 0, f(x) is equal to 20 that is the initial position.
and fot the maximun values of x will be when f(x) = 120
\(120=50x+20\)and we solve for x
\(\begin{gathered} 120-20=50x \\ 100=50x \\ \frac{100}{50}=x \\ 2=x \end{gathered}\)so the domain will be:
\(0\le x\le2\)B) What is the cost of making 35 items?
And c. The domain
The cost of making 35 items is 1100 and the domain is (-∞,∞)
The cost of making 35 items :
x = 35plug the value into the cost equation
C(35) = 10(35) + 800
C(35) = 350 + 800
C(35) = 1100
Hence, cost of making 35 items is 1100
The domain of the functionSince the value of X can be any real number, we can plug in any real number for x and get a real number output.
Hence, the domain = (-∞,∞)
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Belinda is making bracelets for an auction fundraiser. The number of beads varies directly with the number of inches of string used to make the
bracelets. Use the information in the table to write an equation.
Number of Inches of String.
X
+
I
x
+
2
4
6
8
old
ď vo vo
Number of Beads,
y
18
36
54
72
2
(0)
11
The equation representing the number of beads varies directly with the number of inches of the string is y = 9x.
What are ratio and proportion?In its most basic form, a ratio is a comparison between two comparable quantities.
There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.
If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.
Given, The number of beads varies directly with the number of inches of string.
Therefore, y ∝ x.
y = kx.
From the table,
18 = 2k.
k = 9.
So, y = 9x.
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AABC and AXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the thiside of each triangle.A6.5X3.6B5.2YZCProvide your answer below:MORE INSTRUCTIONayFEEDBACK4.5SUBMIT
Since the triangles are similar this means that the ratios between similar sides have to be equal; this means that:
\(\begin{gathered} \frac{6.5}{3.6}=\frac{5.2}{y} \\ \frac{6.5}{3.6}=\frac{a}{4.5} \end{gathered}\)Solving the first equation we have:
\(\begin{gathered} \frac{6.5}{3.6}=\frac{5.2}{y} \\ y=\frac{5.2}{\frac{6.5}{3.6}} \\ y=2.88 \end{gathered}\)Solving the second equation:
\(\begin{gathered} \frac{a}{4.5}=\frac{6.5}{3.6} \\ a=4.5(\frac{6.5}{3.6}) \\ a=8.125 \end{gathered}\)Therefore, a=8.125 and y=2.88
i need help, please
Answer:
\(\frac{51}{4}\)
Step-by-step explanation:
Since they are similar we can set up direct proportions
FE:CB=DE:AB
y:6=17:8
\(\frac{y}{6} =\frac{17}{8}\)
cross multiply
8y=17*6
divide by 8 each side
\(\frac{51}{4}\)
The kettle in Keith,s kitchen is 80% full. After 20% of the water in it has been poured out. There are 1152ml of water left. What volume of water does Keith’s kitchen kettle hold when it is full?
The volume of water that Keith's kitchen kettle holds when it is full is 1800 ml.
Assume that Keith's kitchen kettle has a "x" ml capacity when it is full.
The kettle is initially 80% full, which means it holds 0.8x ml of water, according to the problem.
20% of the water is poured out, leaving 80% of the original amount of water in the kettle, which is:
0.8x * 0.8 = 0.64x ml
We are informed that the 1152 ml of water that is left equates to:
0.64x = 1152
By multiplying both sides by 0.64, we obtain:
x = 1800
Consequently, Keith's cooking kettle has an 1800 ml capacity when it is full.
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Brianna made 9 1/4 bags of popcorn for a movie night with some friends. Together they ate 4 bags of it. How much popcorn was left?
There were 5 1/4 bags of popcorn left after eating 4 bags.
To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.
Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:
9 1/4 = (4 * 9 + 1) / 4 = 37/4
Now, let's subtract the 4 bags eaten from the total:
37/4 - 4
To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:
37/4 - 4/1
Now, let's find a common denominator and subtract the fractions:
37/4 - 16/4 = (37 - 16) / 4 = 21/4
The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:
21/4 = 5 1/4
Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.
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ƒ(t) = –1∕2t2 + 2t + 6
This function represents a downward-opening parabola with a vertical shift of 6 units upward.
How to explain the functionThe given function is Ƒ(t) = –1/(2t²) + 2t + 6.
This is a quadratic function in terms of t. The general form of a quadratic function is f(t) = at² + bt + c, where a, b, and c are constants.
Comparing the given function Ƒ(t) = –1/(2t²) + 2t + 6 with the general form, we can see that a = -1/2, b = 2, and c = 6.
So, the function Ƒ(t) can be written as:
Ƒ(t) = (-1/2)t² + 2t + 6
This function represents a downward-opening parabola with a vertical shift of 6 units upward.
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In a recent survey of 36 people, 18 said that their favorite color of car was blue.
What percent of the people surveyed liked blue cars? Explain your answer with every step you took to get to it.
Answer: The percentage of people surveyed who liked blue cars is 50%.
Step-by-step explanation:
Total number of people partaking in survey= 36
number of people who like blue cars= 18
therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)
hence, percentage of people who liked blue cars= (18/36)*100 %
= 50%
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Answer:
Percentage of people who like blue-coloured cars is 50%
Number of people who were surveyed=36
Number of people who like blue-colored cars=18
Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100
=(18/36)*100
=50%
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Need help please and thank you
Hey!
For any graphing calculator problems I would recommend using desmos if your teacher allows it or getting a graphing calculator such as a ti-nspire :)
This way, it will be able to graph and get the answers quicker!
The answers to this question is (37.5,15) and (0,60). To find your answers when you graph always look for where the lines intersect. If the lines do not intersect then it is not one of your answer choices. (examples are below).
The arrow on the spinner below is spun once
What is the probability the arrow on the spinner does not stop on a number DIVISIBLE by 3? pls help ty
A. 1/8
B. 1/4
C. 3/4
D. 1/8
The probability that the arrow will land on an even number is 1/2.
Option D) 1/2 is the correct answer.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
the probability that the arrow will land on an even number:
Given that;
Total number of Integers on the spinner = 8
Total number f even integers on the spinner = 4
Probability that the arrow will land on an even number = ?
The probability that the arrow will land on an even number will be;
P = Total number f even integers on the spinner / Total number of Integers on the spinner
P = 4 / 8
P = 1/2
Therefore the probability that the arrow will land on an even number is 1/2.
Option D) 1/2 is the correct answer.
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help me easy 20 points!!
Answer:
Step-by-step explanation:
Emily bought seashells from the souvenir shop when she was on vacation. Each seashell cost .75. Emily bought 10 seashells. What was the total cost if the seashells?
Answer:
$7.50
Step-by-step explanation:
Each shell is $0.75. You buy ten. Ten times 0.75 is 7.5
Answer:
$7.50
Step-by-step explanation:
The average daily balance of a credit card for the month of November was $700, and the unpaid balance at the end of the month was $1,400. If the annual percentage rate is 15.6% of the average daily balance, what is the total balance on the next billing date December 1? Round your answer to the nearest cent.
Answer:
Step-by-step explanation:
To calculate the total balance on the next billing date, we need to consider the average daily balance and the unpaid balance from the previous month.
Given:
Average daily balance for November = $700
Unpaid balance at the end of November = $1,400
Annual percentage rate (APR) = 15.6%
Step 1: Calculate the interest charged for the month of November.
Interest = (Average daily balance * APR * Number of days in the month) / 365
Number of days in November = 30
Interest = (700 * 0.156 * 30) / 365 = $36.44 (rounded to the nearest cent)
Step 2: Add the interest to the unpaid balance to get the total balance on December 1.
Total balance = Unpaid balance + Interest
Total balance = $1,400 + $36.44 = $1,436.44
Therefore, the total balance on the next billing date, December 1, is $1,436.44 (rounded to the nearest cent).
The total balance on the next billing date December 1 is $1,509.20.
What is an annual percentage rate?The annual interest produced by a sum that is paid to investors or charged to borrowers is referred to as the annual percentage rate (APR).
Given,
The average daily balance of a credit card for November = is $700Unpaid balance at the end of the month = $1,400The annual percentage rate = 15.6%Then, the percentage rate for November = \(\sf\frac{15.6}{100}\) × 700
\(\sf = \$109.20\)
Balance on 1st December = unpaid balance at the end of November + percentage rate
\(\sf = $1400 +$109.20\)
\(\sf =\$1509.20\)
Therefore, the total balance on the next billing date December 1 is $1,509.20.
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How can 10% of 45 be used to determine 30% of 45?
Enter your answers in the boxes to correctly complete the sta
10% of 45 is
so 30% of 45 is
Answer: 10% of 45 is 4.5
So 30% of 45 is 13.5
Step-by-step explanation:
Write the direct variation function given that y varies directly with x, and y = 1.5 when x = 5.
Answer:
y=0.3x
Step-by-step explanation:
Formula = \(K=\frac{y}{x}\)
y α x
y = kx
Where k is the constant of proportionality.
When y = 1.5; x = 5;
We substitute these known values in the equation,
y = kx
1.5 = k5
Dividing both sides of the equation by 5 to find the value for k, we have
1.5/5= k0.3/5
Therefore,
K = 0.3
Having found the value of k,
We substitute this value into the relationship
y = kx
Therefore we have,
y = 0.3x.
The direct variation function is therefore,
y = 0.3x.
[RevyBreeze]
Answer:
y= 0.3x
Step-by-step explanation:
Since y varies directly as x, use the direct variation equation, y = kx.
1.5 = k(5) Substitute 1.5 for y and 5 for x.
k = 0.3 Solve for k.
Write the direct variation function by using the value for k.
y = 0.3x Substitute 0.3 for k in y = kx.
Find the smallest positive integer k such that, for every positive integer n, 6n+k is relatively prime to each of 6n+3, 6n+2, and 6n+1.
Answer:
Use Mathpapa to find your answer.
Step-by-step explanation:
It's a good, and powerful program.
Question 2 (15 points )
Determine the scale factor from circle A to circle B.
O
Scale factor =
B
30
Thus, the scale factor from circle A to circle B is found to be 2.
Explain about the scale factor:The ratio between comparable measurements of just an element and a portrayal of that element is known as a scale factor in mathematics. The copy will be larger if the scaling factor is a whole number. A fractional scaling factor means that the duplicate will be smaller.
You must first choose which direction we are scaling in order to determine the scale factor:
Scale Up = larger measurement / smaller measurement (smaller to larger).Smaller measurement equals greater measurement when scaling down.The radius of circle A = 2 units
The radius of circle B = 4 units.
So, there is a dilation with the scale factor of 2 units as 2*2 = 4 units.
Thus, the scale factor from circle A to circle B is found to be 2.
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1000 as a power of 10 us equal to what
Answer:
its sounds like this means 10^1000?
the answer would be 1E1000
if it says 1000^10, the answer is 1E30
Finding the Height of an Airplane An aircraft is spotted by two observers who are 1000 feet apart. As the airplane passes over the line joining them, each observer takes a
sighting of the angle of elevation to the plane, as indicated in the figure. How high is the airplane?
The plane is at a height of approximately 381.69 feet.
Answer:
381.69 feet.
Step-by-step explanation:
To find the height of the airplane, we can use the principles of trigonometry. Let's call the distance between each observer and the point directly below the airplane on the ground "x", and let's call the height of the airplane "h".
From observer A, we can see that the angle of elevation to the airplane is 60 degrees. From observer B, we can see that the angle of elevation to the airplane is 30 degrees.
Using trigonometry, we can set up the following equations:
tan(60) = h/x
tan(30) = h/(1000 - x)
Solving for h in both equations, we get:
h = x * tan(60)
h = (1000 - x) * tan(30)
Setting these two expressions equal to each other, we can solve for x:
x * tan(60) = (1000 - x) * tan(30)
x * sqrt(3) = 1000 - x/√3
x = (1000 * √3) / (1 + √3)
Plugging this value of x into either of the original equations, we can solve for h:
h = x * tan(60)
h ≈ 381.69 feet
Therefore, the height of the airplane is approximately 381.69 feet.
What is an equation of the line that passes through the point (−2,1) and is parallel to the line whose equation is 4x − 2y = 8? *
Answer:
since the lines are parallel to each other
m1 = m2( their slopes are equal)
4x - 2y = 8
-2y = 8 -4x
-2y = -4x + 8
divide both sides by -2
y = 2x - 4
since y = mx + c
m = 2
using the formula
y -y1 = m(x - x1)
y - 1 = 2 (x -(-2))
y-1 =2 (x +2)
y -1 = 2x +4
y = 2x +4 +1
y= 2x + 5(equation of the line)
Use the average daily balance method to compute the finance charge on the credit card account
for the month of August (31 days). The starting balance from the previous month is $270. The
transactions on the account for the month are given in the table to the right. Assume an annual
interest rate of 19% on the account and that the billing date is August 1st.
aug 7th. payment of $70
aug. 10 purchase of $135
aug. 15 purchase of $20
aug. 29 purchase of $25
what is the finance charge for the month of August?
The finance charge for the month of August is $4.93.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. Moreover, it is indicated by the symbol "%."
Given:
The starting balance from the previous month is $270.
The transactions on the account for the month are given in the table to the right.
Assume an annual interest rate of 19% on the account and that the billing date is August 1st.
After finding the balance outstanding each day, we sum it up.
And get the average as $305.4839
Now we find the average balance by dividing it by 31 days of the August month.
Average balance = $305.4839
Finance charge = $305.4839 x19 x 31/365 days
Finance charge = $4.929589
Finance charge = $4.93
Therefore, the Finance charge = $4.93.
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Find the polar coordinates of rectangular coordinates (-√2,1). Limit θ to the interval [0,2pi) and round 2 dceimal places if needed
The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.
To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:
r = √(x² + y²)
θ = tan^⁻1(y/x)
Plugging in the given values of (-√2,1), we get:
r = √((-√2)² + 1²) = √(2 + 1) = √3
θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians
Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:
θ ≈ 2.0344 + π ≈ 5.1779 radians
Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).
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Is any real number exactly 2 more than its cube?
Answer: Yes
Step-by-step explanation: The real number, which most exceeds its cube, is A 21
Liam will spin the pointer one time. What is the probability that the pointer will land on red?
Answer:
Step-by-step explanation:
What are the other colors?
if there are two colors ( red and another color ) then the probability of the pointer landing on red will be 1/2
similarly if there are 3 colors ( red and two other colors) then the probability of the pointer landing on red will be 1/3 ....
depends on how many colors are there
The point P=(1/2,y)lies on the unit circle shown below. What is the value of y in simplest form?
The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.
To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.
Plugging in the coordinates of the point P = (1/2, y), we get:
(1/2)^2 + y^2 = 1
1/4 + y^2 = 1
y^2 = 1 - 1/4
y^2 = 3/4.
To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).
Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.
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100 is deposited into an investment account on January 1, 1998. You are given the following information on investment activity that takes place during the year:
April 19,1998 October 30, 1998
Value immediately prior to deposit 95 105
Deposit 2X X
The amount in the account on January 1, 1999 is 115. During 1998, The annual effective dollar weighted yield is 0%, and the annual effective time weighted yield is y. Calculate y.
Answer:
y = - 0.681 % ≈ -0.7 %
Step-by-step explanation:
Given:
April 19,1998 October 30, 1998
Value immediately prior to deposit 95 105
Deposit 2X X
amount in the account on January 1, 1999 = 115
effective dollar weighted yield = 0%
annual effective time weighted yield = y
To find:
Calculate y
Solution:
Given that the dollar weighted return is 0%
100 is deposited into investment account on January 1, 1998. So, add 100 to the deposits 2X X
100 + 2x + x = 115
3x = 115 - 100
3x = 15
x = 15/3
x = 5
Compute y
1 + y = (95/100)(105/105)(115/110)
1 + y = 0.95 * 1 * 1.045
1 + y = 0.99318
y = 0.99318 - 1
y = - 0.0068 * 100
y = - 0.681 % ≈ -0.7 %
y = -0.7 %
There exist integers min such that m minus n is less tha or equal to m plus n.
Answer:
I have asked question in my profile please tell me that answer please
Nicholas put 1,012 baseball cards into boxes. He put 22 cards in each box. How many boxes did Nicholas need for these baseball cards?
Answer:
46 boxes
Step-by-step explanation:
1012 / 22 = 46
3. Higher Order Thinking The
lengths of the pencils are
given at the right.
Write and solve a two-step
problem about the pencils.
6 cm
8 cm
10 cm
The lengths of the three pencils form a right-triangle, and the two-step problem is:
6^2 + 8^2 = 10^2100 = 100How to write the two-step problemThe lengths of the pencils are given as:
6cm, 8cm and 10cm
Using the Pythagoras theorem, we have:
6^2 + 8^2 = 10^2
Evaluate the exponents
100 = 100
Hence, the lengths of the three pencils form a right-triangle
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Never mind i got it!
Answer:
OOk
Step-by-step explanation: