Answer:
Steplo-by-step explanation:loan is 1200.
The interest rate is 6.50
Pp 46.90
Cumulative payment $53.4
Total payments$1,282.93
Final answer:
Lane will pay a total of $156 in simple interest on the loan of $1200 over 2 years, calculated using the simple interest formula: I = PRT.
Explanation:
Lane borrowed $1200 at a simple interest rate of 6.5% for a period of 2 years. To calculate the total amount of interest that will be paid on the loan, we can use the simple interest formula, which is:
I = PRT
where I is the interest, P is the principal amount borrowed, R is the interest rate per year (expressed as a decimal), and T is the time in years the money is borrowed for.
First, we convert R to a decimal by dividing it by 100:
R = 6.5% / 100 = 0.065
Next, we substitute the values into the formula:
I = $1200 × 0.065 × 2
I = $1200 × 0.13
I = $156
Therefore, the total amount of interest that Lane will be paying on the loan over the next 2 years is $156.
Bryan purchases a new boat. The expression below represents the value of the boat after x years. 22000(0.88)^(X+2)
Which statement is true?
The price of the boat decreases by 88% every year.
The price of the boat increases by 88% every year.
The price of the boat decreases by 12% every year.
The price of the boat increases by 12% every year.
None of the above. All the answers refer to price. The given equation refers to value. We imagine price may stay the same or actually increase year-to-year. The problem statement gives insufficient information to conclude anything about price.
Math is about attention to detail. The equation tells you ...
... The value of the boat decreases by 12% every year.
Step-by-step explanation:The value of the boat is multiplied by 0.88 each time X increases by 1. That means the value is 88% of what it was the year before, a decrease of 12%.
1/3(y+7)=(y-1) y= what?
Answer:
y=5
Step-by-step explanation:
1/3(y+7)=(y-1)
I will multiply by 3 on each side to get rid of the fractions
3*1/3(y+7)=(y-1)*3
y+7 = 3*(y-1)
Distribute the 3
y+7 = 3y -3
Subtract y from each side
y-y+7 = 3y-y-3
7 = 2y-3
Add 3 to each side
7+3 = 2y-3+3
10=2y
Divide each side by 2
10/2 = 2y/2
5 =y
In trapezoid ABCD with bases AB and DC , diagonals intersect at point O. Find the length of diagonal BD , if BO=6 cm and: AO/OC = 3/1
Answer:
8 cm
Step-by-step explanation:
... BO/OD = AO/OC = 3/1
Written another way, this is ...
... OD : BO = 1 : 3
Now, BD = OD + BO, so we have
... BD : BO = (OD +BO) : BO = (1 +3) : 3 = 4 : 3
That is, BD = 4/3 × BO
... BD = 4/3 × 6 cm = 8 cm
To find the length of diagonal BD in trapezoid ABCD, we set up an equation using the fact that the diagonals bisect each other. We solve for x and then substitute it into the equation for BD.
Explanation:To find the length of diagonal BD in trapezoid ABCD, we can use the fact that the diagonals of a trapezoid bisect each other. Let AO = 3x and OC = x. Since the diagonals intersect at point O, we can set up the equation (3x + 6) / x = 3 / 1. Solving for x, we find that x = 1.5. Therefore, BD = 2 * x + 6 = 2 * 1.5 + 6 = 9 cm.
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Suppose a fair six-sided is rolled three times in a row. The probability of rolling a number less than 3 three times in a row is __________ . Express the probability as a fraction.
Answer:
1/27
Step-by-step explanation:
The probabaility of rolling a number less than 3 is 2/6 = 1/3, since only two of the six numbers are less than 3.
Assuming the die rolls are independent, the probability of doing this 3 times is the product of the probabilities of doing it each time:
... (1/3)^3 = 1/27
1# Find the missing variable (s). Round to the nearest tenth.
Answer:
7.9
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship of the hypotenuse and the side opposite an angle:
... Sin = Opposite/Hypotenuse
For your geometry, this is ...
... sin(21°) = x/22
Multiplying by 22 gives ...
... x = 22·sin(21°) ≈ 7.9
Write the expression as a difference of a monomial and a trinomial: 2a^4+5a^3-2a^2+4
(2a^4+5a^3+4) -2a^2
Step-by-step explanation:There are 4 terms. Your trinomial could consist of any three of them. Here, we've chosen to use the one with the negative sign as the monomial, because the question asks for a difference.
Please help!!!!! I attached the picture of the full question
Drag each value to the correct location on the tree diagram. Not all values will be used.
$90 $27.84 $66.32 $46.8 $38.48 $29.12 $31.24
See the attachment
Step-by-step explanation:The expected value of store card transactions will be the product of their average value ($58) and their probability of occurrence (48%).
... $58 × 0.48 = $27.84
Transactions are either "store card" or "without a store card", so the probability of a transaction being made without a store card is
... 1 - 0.48 = 0.52
Using the same computatation as for store card expected value, the expected value of transactions made without a store card is ...
... $74 × 0.52 = $38.48
The expected value of the store's transactions is the sum of the expected values of the different ways transactions can be made:
... $27.84 +38.48 = $66.32
_____
The average value of transactions made without a store card is the weighted average of those made with another card and those made with cash or a gift card. Using c to represent the latter, this weighted sum is ...
... 74 = 0.80 × 70 + 0.20 × c
... 74 -56 = 0.20c . . . . . subtract 56
... 18/0.2 = c = 90 . . . . . divide by the coefficient of c
The average transaction made with cash or a gift card is $90.
Each expected value per transaction should be matched to the correct location on the tree diagram as shown in the image below.
How to determine the expected value per transactions?In this exercise, we would use probability to make each of the decisions. The expected value for transactions made with a store card can be determined by multiplying its probability of occurrence (48%) by the average value ($58) as follows;
Expected value per transaction = 58 × 0.48
Expected value per transaction = $27.84
Since transactions are either made with a store card or without a store card, the probability of a transaction being made without a store card is given by;
Probability (without a store card) = 1 - 0.48 = 0.52
In this context, the expected value per transactions made without a store card is given by;
Expected value per transaction = 74 × 0.52
Expected value per transaction = $38.48
... $74 × 0.52 = $
For the store's expected value transactions, we would add each of the expected values calculated above;
Store's expected value transactions = 27.84 + 38.48
Store's expected value transactions = $66.32.
The average transaction value for transactions that are made with cash or a gift card can be calculated by finding the weighted average of all transactions made without a card;
74 = (0.80 × 70) + 0.20 × m
74 = 56 + 0.20m
0.20m = 74 - 56
0.20m = 18
m = 18/0.20
m = $90.
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Solve each of these systems using the substitution method. Make sure to check your answers !
2x + 3y = -4
x − 2y = 5
a. x = 1, y = -2
b. x = -1, y = 2
c. x = 1, y = 2
d. x = -2, y = -1
Answer:
a. x = 1, y = -2
Step-by-step explanation:
The given equations are 2x + 3y = -4 -------------(1)
x - 2y = 5 -----------------(2)
From the second equation, we get x = 2y + 5
Now plug in x = 2y + 5 in the first equation, we get
2(2y + 5) + 3y = - 4
4y + 10 + 3y = -4
7y + 10 = -4
7y = -14
y = -2
Now plug in y = -2 in x = 2y + 5 to find the x value.
x = 2(-2) + 5
x = -4 + 5
x = 1
Therefore, x = 1, y = -2
Thank you.
You and your friend leave your houses at the same time to meet at a restaurant. The distance (in miles) your friend is from the restaurant is given by y=-70x+140,where x is the number of hours since your friend left home. You live 80 miles from the restaurant and arrive at the same time as your friend. Write a linear equation that represents your distance from the restaurant.
Answer:
y = 80 -40x
Step-by-step explanation:
The given equation shows the friend arrives at the restaurant (y=0) when x=2. That is, half the initial distance to the restaurant is covered in each hour of travel time.
If I take 2 hours to travel the 80 miles from my house, my distance will decrease at the rate of 40 miles per hour. My distance from the restaurant can be represented by ...
... y = -40x +80
Kohls is offering a special discount promotion. A merchandise order totaling less than $25 will receive a 25% discount, and an order totaling $25 or more will receive a 50% discount. Which of these correctly describes purchases made at the store during this promotion? Select all that apply.
A A purchase of 3 pairs of socks selling for $4 a pair will be charged as $9 after the promotion is applied.
C A purchase of 3 pairs of skirts selling for $8 each will be charged as $6 after the promotion is applied.
D A purchase of 3 video games selling for $32.45 each will be charged as $48.68 after the promotion is applied.
B A purchase of 1 pair of shoes selling for $78 will be charged as $58.50 after the promotion is applied.
What is the best approximation of the length of segment QS? (Note: cos 80° = 0.17)
(Round your answer to the nearest tenth.)
Answer: [tex]QS=11.8cm[/tex]
Step-by-step explanation:
1. You have the following information:
- The lenght of [tex]RS[/tex] is 2 centimeters.
- The angle m∠S=80°.
- Cos80°=0.17
2. Therefore, you can calculate the lenght of the segment [tex]QS[/tex] as following:
[tex]cos80=\frac{adjacent}{hypotenuse}[/tex]
[tex]adjacent=2cm\\hypotenuse=QS\\cos80=0.17[/tex]
3. Substitute values and solve for [tex]QS[/tex]:
[tex]0.17=\frac{2cm}{QS}\\QS=\frac{2cm}{0.17} \\QS=11.76cm[/tex]
4. To the nearest tenth:
[tex]QS=11.8cm[/tex]
You are tired at the end of the term and decide to borrow $500 to go on a trip to whatever land. You go to the bank and borrow the money at 11% for 2 years. A) find the interest you will pay on the loan. B) how much will you have to pay the bank at the end of the two years ?
Answer:
A)55
B)110
Step-by-step explanation:500 /11%=55
55*2=110
The interest is $110 and the amount paid to the bank is $610.
What is simple interest?Simple interest is calculated just on the loan's principal amount, whereas compound interest is calculated on both the principal and the cumulative interest.
It is given that you decide to borrow $500 to go on a trip to whatever land. You go to the bank and borrow the money at 11% for 2 years.
A. The simple interest is,
SI = ( Principle x rate x time ) / 100
SI = ( 500 x 11 x 2 ) / 100
SI = $110
B. The amount paid to the bank after 2 years is,
Amount = P + SI
Amount = $500 + $110 = $610
Therefore, the interest is $110 and the amount paid to the bank is $610.
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What transformations change the graph of f(x) to the graph of g(x)? f(x) = 3x2 g(x) = 9x2 - 4
Question 2 options:
The graph of g(x) is the graph of f(x) stretched vertically by a factor of 1/3 and translated up 4 units.
The graph of g(x) is the graph of f(x) stretched vertically by a factor of 1/3 and translated down 4 units
. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated up 4 units.
The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated down 4 units.
Answer:
D.
Step-by-step explanation:
The coefficient of the leading term tells you how "stretchy" a graph is. Since g(x)'s leading coefficient is 3, and f(x)'s leading coefficient is 9, and they're both [tex]x^{2}[/tex], g is just 3 times f. Then g's constant term is -4, and f's constant term is 0, then g is just f but translated 4 down.
Answer:
Option 4
Step-by-step explanation:
The 3 changing to the 9 stretches the graph vertically by a factor of 3. The - 4
translates the graph 4 units down .
Its Option 4
The sum of the measures of the angles shown is 63° . Which choice is the measure of angle y ?
Answer:
63
Step-by-step explanation:
Answer:
25 degrees.
Step-by-step If one of the angles is 38 degrees then in order for the sum to be 63, the answer is 25
What is the fraction in decimal form?
21/6
Enter your answer in the box
Answer: Your answer would come out to be 3.5
Step-by-step explanation: it would be 3.5 due to the fact that you have to break these numbers down to the smallest one possible meaning simplify which would result in this equation 7 over 2
7 over 2 = 3 1 over 2 this equals 3.5
Evaluate f(3) x(5x-9)
I think I have the answer just now sure thanks if you can help
18
Step-by-step explanation:Put 3 where x is, then do the arithmetic.
... f(x) = x(5x -9)
... f(3) = 3(5·3 -9) = 3(15 -9) = 3·6
... f(3) = 18
_____
Your calculator can do this, too.
Use your classmates to write 5 or more ratios. For example, you could compare boys to girls or people with glasses to people without glasses.
Answer:
1/3 3/1 5/6 6/5 8/9 9/8
Step-by-step explanation:
f(x) = (x+2)(x-1)(2x+3)
Which statements are true? (Graph is pictured)
Select ALL that apply
A)The end behavior of functions f(x) and g(x) are exactly the same.
B)Both functions have exactly three x-intercepts.
C)The function f(x) is an odd degree function.
D)The function g(x) has a positive leading coefficient.
E)The x intercepts for g(x) are (1, 0); (2, 0) and (-3/2, 0)
Answer:
B) Both functions have exactly three x-intercepts.
C) The function f(x) is an odd degree function.
E) The x intercepts for g(x) are (1, 0); (2, 0) and (-3/2, 0)
Step-by-step explanation:
The function f is a function of degree 3 (there are 3 x-terms in the product contributing to the highest-degree term), so is of odd degree. The leading coefficient in f(x) is the product of the coefficients of x: 1·1·2 = 2, a positive number.
For a polynomial function of odd degree, the general shape of the graph will be "/" if the leading coefficient is positive, and "\" if the leading coefficient is negative. That is, end behaviors will be opposites of each other. Function f has a positive leading coefficient, so its end behavior will be (-∞, -∞) and (+∞, +∞). Function g has end behavior that is (-∞, +∞) and (+∞, -∞), so is not the same. Apparently, g(x) has a negative leading coefficient.
The graph of g(x) shows it to have 3 x-intercepts. They can be read from the graph as (-3/2, 0), (1, 0) and (2, 0). The factoring of f(x) shows it to have 3 x-intercepts, the same number. There is an x-intercept of f(x) for each factor. (The x-intercept value is the value of x that makes the factor zero.)
The function f(x) is of odd degree and has three x-intercepts at -2, 1, and -3/2. The statements regarding the function g(x) cannot be confirmed without further information.
Explanation:The function given is f(x) = (x+2)(x-1)(2x+3). The degree of the function is 3 as there are three terms multiplied together. Therefore, f(x) is an odd degree function, which makes option C correct.
The x-intercepts of the function occur where y = 0, i.e. where f(x) = 0. Solving this will give the roots or intercepts for x which are -2, 1, and -3/2. This means that the function f(x) has three x-intercepts, which makes option B correct.
Without information or a graph of function g(x), we cannot accurately answer options A, D and E. We cannot know the end behavior, the leading coefficient or the x intercepts for g(x). Therefore, only options B and C are true statements.
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I need help answering this question
21 miles
Step-by-step explanation:Big Bird's nest is halfway between Bert's place and Ernie's place, so the distance from the nest to either apartment is the same. Equating those distances, we have ...
... 5x +4 = 15x -30
... 34 = 10x . . . . . . add 30-5x
... 3.4 = x . . . . . . . .divide by 10
The value of x is not the distance. The distance is given by either of the two expressions
5x+415x-30Using the first of these, the distance from either apartment to Big Bird's nest is ...
... 5·3.4 +4 = 17 +4 = 21 . . . . miles
Of course, using the second gives the same answer:
... 15·3.4 -30 = 51 -30 = 21
f(x)=log5 (2x+12)+2 yeah this ome threw me off
Answer:
See below for a graph
Step-by-step explanation:
Let's call the parent function g(x) = log₅(x), which has a vertical asymptote at x=0, and goes through the points (1, 0), (5, 1), (25, 2).
Then this function is
... f(x) = g(2(x+6)) +2
That is, the function is horizontally compressed by a factor of 2, shifted left 6 units, and shifted up 2 units. This moves the points listed above to ...
... (-5.5, 2), (-3.5, 3), (6.5, 4)
The graph shows the parent function and the listed points in blue, then the transformed function and the corresponding points in red.
If m ABC is 53 degrees then m EDF is ?
Answer:
74°
Step-by-step explanation:
The triangle is isosceles and the congruent base angles are 53°. The sum of angles in a triangle is 180°, so the apex angle (∠EDF) will be ...
... 180° - 2×53° = 74°
Answer:
74* is the answer
Step-by-step explanation:
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please hurry thank you
Answer:
7.9 ft
Step-by-step explanation:
The hypotenuse is the side opposite of the right angle, hence the hypotenuse for this triangle is 11 ft.
Side [tex]x[/tex] is adjacent to the angle given. So we need adjacent and we have hypotenuse. Which trigonometric ratio relates adjacent and hypotenuse? It is COSINE.
Thus, we can write:
[tex]cos(A)=\frac{adjacent}{hypotenuse}\\cos(44)=\frac{x}{11}[/tex]
Cross multiplying, we can solve for [tex]x[/tex]:
[tex]cos(44)=\frac{x}{11}\\x=cos(44)*11\\x=7.91[/tex]
Rounding to nearest tenth, we have [tex]x=7.9[/tex] ft.
Ally and Beth are at the grocery store. Ally buys a container of milk for $4 and 4.75 pounds of apples. Beth buys a box of cereal for $3 and 5.55 pounds of apples. If the girls spend the same amount, how much does 1 pound of apples cost?
Answer:
$1.25
Step-by-step explanation:
Whose beaker has the least amount of liquid in it.
Jay 0.8
Alana 1.05
Evan 1.2
Stacey 0.75
The equation C = 5/9(F - 32) is used to convert between Fahrenheit temperatures and Celsius temperatures. The temperature in Augusta on a summer day is 33° C.
Rounded to the nearest whole number, what is the temperature in Fahrenheit?
A) 55°F
B) 68°F
C) 79°F
D) 91°F
Answer:
D) 91 °F
Step-by-step explanation:
C = 5/9(F - 32)
33 = 5/9 (F – 32) Multiply each side by 9
9×33 = 5(F- 32) Divide each side by 5
9×33/5 = F – 32 Add 32 to each side
F = 9×33/5 + 32
F = 59.4 + 32
F = 91 °F
Answer:
Its D
Step-by-step explanation:
USA TP
Julie wants to make a handmade Valentines she buys 1/2 yard of red ribbon and 3/4 yard of pink if each Valentine needs 1/8 yards how many can she create please show you work will Mark rainiest and we'll add you to help suow work
Answer:
10 Valentines
Step-by-step explanation:
1/2 = 4/8
3/4 = 6/8
Julie has a total of 4/8 + 6/8 = 10/8 yards of ribbon. If color doesn't matter, she can make 10 Valentines.
_____
10/8 = 10 × 1/8
Find a polynomial, which if substituted for M will make the equation an identity: (4c^2–7c^2+6)–M=0
Answer:
-3c^2 +6
Step-by-step explanation:
The equation will be an identity (0=0) when M is equal to the contents of the parentheses. That polynomial can be used directly, or it can be simplified by combining the c^2 terms.
The contents of parentheses simplify as follows:
... (4c^2 -7c^2 +6) = (c^2(4 -7) +6) = (-3c^2 +6)
Answer:
4c^4-7c^2+6
Step-by-step explanation:
A geometric sequence is shown below 2,-6,18,-54,162,... part A: what a recursive relationship for this sequence. Explain how you determined your answer part B: write an explicit formula for this sequence
A) The problem statement tells you it is a geometric sequence, so you know each term is some multiple of the one before. The first terms of the sequence are given, so you know the first term. The common ratio (the multiplier of interest) is the ratio of the second term to the first (or any term to the one before), -6/2 = -3.
So, the recursive definition is ...
... a_1 = 2
... a_n = -3·a_(n-1)
B) The explicit formula is, in general, ...
... a_n = a_1 · r^(n -1)
where r is the common ratio and a_1 is the first term. Filling in the known values, this is ...
... a_n = 2·(-3)^(n-1)
Answer:
a1=2
an=(an-1)(-3)
Step-by-step explanation:
Hope it helps. :)
Liam volunteers to help plan the event. The first month, he volunteered for x hours. The next month he volunteered for 1 2/3 times as many hours as he had the first month. If he volunteered for a total of 40 hours, how many hours did he volunteer during the first month? Write an equation to represent the situation and solve.
To find the number of hours Liam volunteered during the first month, we can set up an equation using the given information. By solving the equation, we find that Liam volunteered for 15 hours during the first month.
Explanation:To solve this problem, we can start by representing the number of hours Liam volunteered in the first month as x. The number of hours volunteered in the next month would be 1 2/3 times x, which can be written as (5/3)x. The total number of hours volunteered is given as 40, so we can write the equation: x + (5/3)x = 40. To solve for x, we can combine the like terms and solve the resulting equation.
Combining the x terms, we get (8/3)x = 40. Solving for x, we divide both sides of the equation by 8/3: x = 40 / (8/3).
Simplifying, we have x = 40 * (3/8) = 15. Therefore, Liam volunteered for 15 hours during the first month.
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By representing the number of hours in the first month as x, we can find the value of x by using the given information and solving the equation. The solution shows that Liam volunteered for 15 hours during the first month.
Explanation:To solve this problem, we can set up an equation representing the total number of hours Liam volunteered. Let's represent the number of hours he volunteered in the first month as x. According to the problem, he volunteered for 1 2/3 times as many hours in the next month. So, the number of hours he volunteered in the next month is 1 2/3 x. The total number of hours is given as 40. Therefore, we have the equation:
x + 1 2/3 x = 40
To solve for x, we can simplify the equation by converting 1 2/3 to an improper fraction. This gives us:
5/3 x + 1 2/3 x = 40
Combining like terms, we get:
8/3 x = 40
To solve for x, we can multiply both sides of the equation by the reciprocal of 8/3, which is 3/8. This gives us:
x = (40)(3/8) = 15
Therefore, Liam volunteered for 15 hours during the first month.
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please help me asap!