Answer:
A) 1: exponential; 2: linear
B) 1: f(x) = 45000·0.9^x; 2: f(x) = -3000x+45000
C) The difference is significant. 1: $11,348; 2: $6,000
Step-by-step explanation:
Part AThe values for Car 1 have a common ratio of 40500/45000 = 0.9. An exponential function is used to describe a sequence where the terms have a common ratio.
The values for Car 2 have a common difference of 42000-45000 = -3000. A linear function is used to describe a sequence where the terms have a common difference.
__
Part BAn exponential function can be written as ...
f(x) = (initial value)·(common ratio)^x
A linear function can be written as ...
f(x) = (common difference)x + (initial value)
The functions are ...
Car 1: f(x) = 45000·0.9^x
Car 2: f(x) = -3000x +45000
___
Part CThe formulas for the different car values after 13 years give ...
Car 1: f(13) = 45000·0.9^13 ≈ 11,348
Car 2: f(13) = -3000(13) +45000 = 6,000
The value of Car 1 will be almost double the value of Car 2 after 13 years. Yes the difference in value is significant.
Rico had $80. He spent 40% on snacks and 1/4 on travel and kept 1/2 of the remainder for the next day.
Answer:
$4????
Step-by-step explanation:
I searched 40% of 80 and got 32, then 1/4 of 32, which was 8, then that in half was 4. I am not sure if it is right or if 8 was the final answer.
In which quadrant does the angle t lie if tan(t)>0 and cos(t)<0?
A) II
B) IV
C) Cannot be determined
D) III
E) I
Quadrant is a quarter of a coordinate plane
The location of angle t is in quadrant 3
The trigonometry equations are given as:
tan(t)>0 and cos(t)<0
The cosine of an angle is negative in the following quadrants
Quadrant 2Quadrant 3The cosine of an angle is positive in the following quadrants
Quadrant 3The intersection of the above points is quadrant 3
This means that the angle is in quadrant 3
Hence, the true option is (D) III
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please help me calculation completing square?
x²+2x-24=0?
Answer:
x = 4, -6
Step-by-step explanation:
x = 4, -6
A radioactive substance decays exponentially. A scientist begins with 150 milligrams of a radioactive substance. After 20 hours, 75 mg of the substance remains. How many milligrams will remain after 27 hours?
Answer:
Step-by-step explanation:
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=21(0.97)^x
what is the % increase
Answer:
Step-by-step explanation:
As the number under the exponent is less than 1, this is a decay function.
y decreases by (1 - 0.97)100 = 3% for each unit increase in x
so the increase would be -3%
solve pls brainliest
Answer:
1. -64
2.-27
Step-by-step explanation:
Hopes this helps
:)
Calculate the volume of the pyramid. Round your answer to the nearest hundredth 10in 7in
Answer:
Place the numbers in their places. b=base h=height.
Step-by-step explanation:
Find an expression that gives you a quotient
of 16
Answer: Does 32/2 work it equals 16
Step-by-step explanation:
The number expression would be 32/2 which gives 16 after applying the arithmetic operation.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
It is given that:
The quotient is 16
Let us assume 32 and 2 are the numbers that can be use in the number expression
The number expression is:
= 32/2
= 16
Thus, the number expression would be 32/2 which gives 16 after applying the arithmetic operation.
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12.) Samuel is 30.75 inches tall. His younger brother, Spencer, is 6 inches shorter. How tall is Spencer?
Answer: Spencer is 24.75 inches tall
Step-by-step explanation: Just subtract 6 from 30.75 to find the answer
Answer:
The percentage increase in Spencer's height is 125%
Step-by-step explanation:
Solution:
Initial height of spencer = 28 inches
Increased height of spencer = 5 feet 3 inches
= 5 feet + 3 inches
(5 feet = 5 ×12=60 inches)
= 60 + 3
Một người tiêu dùng có thu nhập I = 1.200 đ dùng để mua hai sản phẩm X và Y với giá tương ứng là PX = 100đ/sp và PY = 300đ/sp. Mức thoả mãn được thể hiện qua hàm số:
TUX = -1/3X2 + 10X
TUY = -1/2Y2 + 20Y
a. Hãy xác định phương án tiêu dùng tối ưu của người này?
b. Tính tổng hữu dụng tương ứng đạt được?
gak bisa bahasa inggris.
Step-by-step explanation:
maap.
Please verify how [tex]\frac{1-cos(x)}{sin(x)} =\frac{sin(x)}{1+cos(x)}[/tex]
Answer/Step-by-step explanation:
[tex]\frac{1-\cos \left(x\right)}{\sin \left(x\right)}=\frac{\sin \left(x\right)}{1+\cos \left(x\right)}[/tex]
When you have an equation like this, you can start from either side. So, let us start from the left side.
[tex]\underline{\mathrm{Left\:side:}} \quad\frac{1-\cos \left(x\right)}{\sin \left(x\right)}[/tex]
[tex]\sf{Rewrite\: using \:Trig \:identities=\frac{\sin \left(x\right)}{1+\cos \left(x\right)}}\\\\\mathrm{Therefore,\: it \:is \:true}[/tex]
Can someone please help me with #14 and #15?
14.Given y=2(x - 10)+3, write an equation in point slope and slope intercept form that is:
a) Parallel and goes through (-4,1).
b) Perpendicular and goes through (-4,1).
15.Given 5x+2y=7
a.Find an equation parallel to the equation and through (0,10).
b.Find an equation perpendicular to the equation and through (0,10).
This picture is an example of what the answers should look like.
Problem 14, Part (a)
The given equation y = 2(x-10)+3 has a slope of m = 2. Anything parallel to this will also have the same slope, but a different y intercept.
Let's find the point slope form of the parallel line through (-4,1)
[tex]y-y_1 = m(x - x_1)\\\\y-1 = 2(x - (-4))\\\\y-1 = 2(x + 4)\\\\[/tex]
The point slope form is: y-1 = 2(x+4)Now solve for y to get the slope intercept form.
[tex]y-1 = 2(x + 4)\\\\y = 2(x + 4)+1\\\\y = 2x + 8+1\\\\y = 2x + 9\\\\[/tex]
The slope intercept form is: y = 2x+9============================================================
Problem 14, Part (b)
The original slope is m = 2. Apply the negative reciprocal to go from 2/1 to -1/2. The perpendicular slope is -1/2.
Using the same point (-4,1), we find that the point slope form is...
[tex]y-y_1 = m(x - x_1)\\\\y-1 = -\frac{1}{2}(x - (-4))\\\\y-1 = -\frac{1}{2}(x+4)\\\\[/tex]
The point slope form is: y-1 = (-1/2)*(x+4)Now solve for y
[tex]y-1 = -\frac{1}{2}(x+4)\\\\y = -\frac{1}{2}(x+4)+1\\\\y = -\frac{1}{2}x-2+1\\\\y = -\frac{1}{2}x-1\\\\[/tex]
The slope intercept form is: y = (-1/2)x - 1============================================================
Problem 15, Part (a)
Anything parallel to Ax+By = C will be in the form Ax+By = D. The only thing changes is the C becomes D, where [tex]C \ne D[/tex]. If C = D, then we'd be talking about the exact same line rather than two parallel lines.
We're given 5x+2y = 7. The answer is in the form 5x+2y = D. Plug in (x,y) = (0,10) to find the value of D
5x+2y = D
D = 5x+2y
D = 5(0)+2(10)
D = 20
The equation 5x+2y = D updates to 5x+2y = 20
Answer: 5x+2y = 20============================================================
Problem 15, Part (b)
If you are given Ax+By = C, then anything perpendicular to this is Bx-Ay = D. Here it's possible that C = D; however, it's likely that they'll be different.
The given equation 5x+2y = 7 is perpendicular to anything of the form 2x-5y = D. We'll plug in the given point to find D.
2x-5y = D
D = 2x-5y
D = 2(0)-5(10)
D = -50
Answer: 2x-5y = -50Please help! Cant figure this one out!
Answer:
20.5
Step-by-step explanation:
Given that shapes are similar:
45 = 2x + 4 subtract 4 from both sides
41 = 2x divide both sides by 2
20.5 = x
What’s the slope of 10,6 and 4, 1.2
let's firstly change the 1.2 to a fraction
[tex]1.\underline{2}\implies \cfrac{12}{1\underline{0}}\implies \cfrac{6}{5} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{10}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{\frac{6}{5}}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{\frac{6}{5}}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{10}}}\implies \cfrac{~~ \frac{6-30}{5}~~}{-6}\implies \cfrac{~~ \frac{-24}{5}~~}{-6}\implies \cfrac{~~ -\frac{24}{5}~~}{-\frac{6}{1}}[/tex]
[tex]-\cfrac{\stackrel{4}{~~\begin{matrix} 24 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{5}\cdot -\cfrac{1}{\underset{1}{~~\begin{matrix} 6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \boxed{\cfrac{4}{5}}[/tex]
15. A farmer records the number of eggs that chickens on the farm produce each week. The table
shows the results.
143
160
117
137
152
108
128
If during the next week, the chickens on the farm produce 60 eggs, which statement is true?
A The value 60 is an outlier that will skew the data to the left.
B The value 60 is an outlier that will skew the data to the right.
С The value 60 is not an outlier, and it will not skew the data in either direction.
D
The value 60 is not an outlier, and the effect on the data is unknown.
PLEASE HELPPP!! I need help with both questions
9514 1404 393
Answer:
borrow: $21,056.60interest: $1,983.40Step-by-step explanation:
The relation between the monthly payment (A) and the principal borrowed (P) is ...
A = P(r/12)/(1 -(1 +r/12)^-n)
where the annual interest rate is r and n is the number of monthly payments.
Then the principal P can be found as ...
P = $384(12/0.036)(1 -(1 +0.036/12)^-60) ≈ $21,056.60 . . . loan amount
The sum of payments is ...
$384 × 60 = $23,040.
The difference between the payments made and the loan principal amount is the interest paid:
$23,040.00 -21,056.60 = $1,983.40 . . . total interest
okay this is what i need help with its kinda easy
Answer:
B is the answer .......+4+$#88#!$
A restaurant has total of 60 tables . Of those tables , 38 are round and 13 are located by the window . There are 6 round tables by the window . If tables are randomly assigned to customers , what is the probability that a customer will be seated at a round table or by the window
Answer:
The probability that a costumer will be seated at a round table are 44/60 and the probability that he will be seated by the window is 13/60
The probability that a customer will be seated at a round table is [tex]\frac{19}{30}[/tex] and by the window is [tex]\frac{13}{60}[/tex].
What is Probability ?Probability is a ratio of the number of favorable outcomes to the number of possible outcomes of the experiment.
Probability [tex]=\frac{Number \ of\ outcomes}{Number\ of\ possible\ outcome}[/tex]
We have,
Total number of tables [tex]=60[/tex]
Number of round tables [tex]=38[/tex]
Number of tables located by the window [tex]=13[/tex]
Number of round tables located by the window [tex]=6[/tex]
Now,
Number of possible outcomes customer will be seated at a round table [tex]=38[/tex]
So,
Probability of seated at a round table [tex]=\frac{Number \ of\ outcomes}{Number\ of\ possible\ outcome}[/tex]
[tex]=\frac{38}{60}=\frac{19}{30}[/tex]
Now,
Number of possible outcomes customer will be seated by the window [tex]=13[/tex]
Probability of seated by the window[tex]=\frac{Number \ of\ outcomes}{Number\ of\ possible\ outcome}[/tex]
[tex]=\frac{13}{60}[/tex]
So, probability that a customer will be seated at a round table is [tex]\frac{19}{30}[/tex] and by the window is [tex]\frac{13}{60}[/tex].
Hence, we can say that the probability that a customer will be seated at a round table is [tex]\frac{19}{30}[/tex] and by the window is [tex]\frac{13}{60}[/tex].
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Juan wants to buy a video game for $63. He saves $12 every Friday. Part A. Create an equation to represent Juan's total savings, y, in dollars, after x Fridays. y
Answer:
Answer in explanation.
Step-by-step explanation:
An equation to represent Juan's total savings y, in dollars, after x Fridays will be;
⇒ y = 12x
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Juan wants to buy a video game for $63.
And, He saves $12 every Friday.
Now,
Let total dollars after x Friday = y
And, He saves $12 every Friday.
So, We can formulate;
⇒ Total money (y) = 12x
⇒ y = 12x
Thus, An equation to represent Juan's total savings y, in dollars, after x Fridays will be;
⇒ y = 12x
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1. Andrea’s car has broken down for the third time this month, and she has decided to buy a different car. Her dream car, a 2016 Chevrolet Camaro, costs $38,000. She has a $4,000 down payment saved, and the bank is offering 3.00% APR on 60 month loans for new cars.
a. How much will Andrea need to borrow to buy the Camaro?
b. What would Andrea need to type in Excel to figure her monthly payment, and what will her monthly payment be?
c. What will the total of all of Andrea’s payments be over the lifetime of the car loan?
d. How much will Andrea pay in interest over the lifetime of the car loan?
A) Andrea will need to borrow $34,000 to buy the Camaro
B) Andrea will need to type =(34000x1.03 ^ 5) / 60 in Excel to figure her monthly payment, which will be $656,92.
C) The total of all of Andrea’s payments be over the lifetime of the car loan will be $39.415,31
D) Andrea will pay $5415.31 in interest over the lifetime of the car loan
Since Andrea's car has broken down for the third time this month, and she has decided to buy a different car, and her dream car, a 2016 Chevrolet Camaro, costs $ 38,000, and she has a $ 4,000 down payment saved, and the bank is offering 3.00% APR on 60 month loans for new cars, to determine A) how much will Andrea need to borrow to buy the Camaro; B) what would Andrea need to type in Excel to figure her monthly payment from her, and what will her her monthly payment be from her; C) what will the total of all of Andrea’s payments be over the lifetime of the car loan; and D) how much will Andrea pay in interest over the lifetime of the car loan, the following calculations must be performed:
A) 38000 - 4000 = X 34000 = X
B) = (34000x1.03 ^ 5) / 6039.415,31 / 60656,92C) 34000 x 1.03^5 = X34000 x 1.1592 = X39.415,31 = XD) (34000 x 1.03^5) - 34000 = X(34000 x 1.1592) - 34000 = X39415.31 - 34000 = X5415.31 = X
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Identify the initial amount a and the rate of growth r (as a percent) of the exponential function f(t) = 1500(1.074)t. Evaluate the
function when t=5. Round your answer to the nearest tenth.
A=
R=%
When t=5, f(5)=
The initial amount is the first number = 1500
Rate of growth is inside the parentheses and is added to 1, the rate of growth is 7.4%
Replace t with 5 and solve
1500(1.074) ^5 = $2143.45
Answer:
The growth rate is 7.4% and the initial amount is 1500. The answer when t=5 is 2143.45.
Step-by-step explanation:
Assuming this is actually supposed to be written as 1500*(1.074)^t, then this equation follows the standard growth form y = A(1+r)^t where A represents the initial amount, r represents the rate as a decimal, and t represents time. This means that 1500 (A) would be the initial amount, and if you subtract 1 from what's inside the paratheses, you will get the r rate as a decimal. To get this as a percent, simply multiply it by 100, so you will get 7.4% as your growth rate.
To find what the answer would be when t = 5, just plug in 5 for the value of t in the equation.
f(5) = 1500*(1.074^5)
f(5) = 1500*(1.42896)
f(5) = 2143.45
A company makes 140 bags.
41 of the bags have buttons but no zips.
48 of the bags have zips but no buttons.
25 of the bags have neither zips nor buttons.
A bag is selected at random.
What is the probability that the bag has buttons?
Answer:
41/140 or approximately 29.29%
Step-by-step explanation:
Divide 41 by 140 to get 0.29285714285, and round it to the nearest hundredths.
Answer:
Step-by-step explanation:
b= buttons
z= zips
b∩z'=41
b'∩z=48
b'∩z'=25
b=?
b= b∩z+b∩z' (law of total probability)
140=b∩z+b∩z'+b'∩z+b'∩z' (if this is confusing draw a venn diagram)
140=b∩z+41+48+25
b∩z=26
26+41= 67
67/140= .478571429
Which equation models this situation?
The sum of 23 and a number is 39.
O A. 23 + x = 39
B. 23 - x = 39
C. 39 + x = 23
O D. 23+ 39 = x
Given h(t) = -2(t+ 5)^2 +4, find h(-8).
Answer:
Substitute -8 as x into the equation.
h(-8)=-2(-8+5)^2+4
h(-8)=-2(-3)^2+4
h(-8)=-2(9)+4
h(-8)=-18+4
h(-8)=-14
:)
Suppose that you take 1000 simple random samples from a population and that, for each sample, you obtain a 95% confidence interval for an unknown parameter. Approximately how many of those confidence intervals will contain the value of the unknown parameter?
Using the interpretation of a confidence interval, it is found that approximately 950 of those confidence intervals will contain the value of the unknown parameter.
A x% confidence interval means that we are x% confident that the population mean is in the interval.
Out of a large number of intervals, approximately x% will contain the value of the unknown parameter.In this problem:
95% confidence interval.1000 samples.0.95 x 1000 = 950
Hence, approximately 950 of those confidence intervals will contain the value of the unknown parameter.
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Maria wrote her 606 word
essay in 20 1/5 minutes. At
what rate is she typing?
Answer:
29.5
Step-by-step explanation:
Multiply 606 and 20.5 and get 29.5.
Im so confused- please help
Step-by-step explanation:
a/q
x + x - 3 + 2x - 9 = 36
4x - 12 = 36
4x = 36 + 12 = 48
x = 48/4 = 12
x = 12
so,
x = 12
x - 3 = 12 - 3 = 9
2x - 9 = 2(12) - 9 = 15
we know,
area = 1/2 × base × height
so,
→ 1/2 × 12 × 9
→ 1 × 6 × 9
→ 54 inches.
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Express 8^-4 using a positive exponents
I need help with the question
Answer:
[tex]A = 25\pi[/tex] or 25 × 3.14 = 78.5m
Step-by-step explanation:
The radius is half of the diameter. So the radius = 5m (10/2)
[tex]A = \pi r^{2}[/tex]
[tex]A = \pi (5^{2} )[/tex]
[tex]A = 25\pi[/tex]
What is the 5th row of Pascal's triangle?
Answer:
Row 5 115 161051
Step-by-step explanation: