The current price of the item = 400 dollars
The price in 8 years from today = 543.23 dollars
Given the rate of inflation = 3.9%
The exponential function modelling the future price, p(t) in t years for a certain item is, [tex]p(t)=400(1.039^t)[/tex]
We have to find the current price of the item. This is given by substituting t = 0 in p(t).
That is, p(0) = 400 x 1 = 400 dollars
Therefore current price = 400 dollars
To find the price of the product in 8 years, substitute t = 8 in p(t).
That is, p(8) = [tex]400(1.039^8)[/tex] = 543.23 dollars
Therefore, the future price of the item in 8 years = 543.23 dollars
The question is incomplete. Find out the complete question below:
If the rate of inflation is 3.9% per year, the future price p(t) (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today. p(t)= 400(1.039^t).Find the current price of the item and the price 8 years from today.
Learn more about exponential function model at https://brainly.com/question/11883692
#SPJ4
- 4 - (-10) Find the difference.
Reason:
-4 - (-10) = -4 + 10 = 6
The two negatives cancel to form a positive.
Here's how to visualize what's going on: Draw a number line. Plot a marker at -4. Then move 10 units to the right and you should arrive at 6. This visually indicates -4+10 = 6
Another way to visualize: Imagine you are on basement level 4 of a tall building. If you move up 10 floors, then you'll arrive at the 6th floor. We treat the ground floor as floor 0. It might help to draw a vertical number line.
When Gavin left his house in the morning, his cell phone battery was partially
charged. The charge remaining in Gavin's battery, as a percentage, can be modeled by
the equation B = 28 - 7t, where t is the number of hours since Gavin left his
house. What is the y-intercept of the equation and what is its interpretation in the
context of the problem?
B is the y- intercept of the equation B = 28 - 7t, where B is the percentage of the battery.
What is a linear graph?
Linear graphs are straight line graphs to represent the relationship between two quantities. This graph helps in depicting a result in single straight lines. There is no use of curves, dots, bars, etc., and a straight line is denoted by the term linear. Let's represent the given example in the form of a data table.
Given equation,
B = 28 - 7t
B represents the battery percentage of the phone.
t represents time,
According to the equation, with passing of time the percentage of the battery drops.
28 is the highest amount of battery present at 0 time hours.
With passage of time the battery decreases.
So, in t = 1 hr,
battery, B = 28 - 7*1 = 28 -7 = 21%
similarly, t = 4 hrs,
B = 28 -7*4 = 28 -28 = 0%
The battery completely drains and becomes 0%
Therefore, B is the y- intercept of the equation B = 28 - 7t, where B is the percentage of the battery.
Read more about linear graph at :
https://brainly.com/question/16937826
#SPJ1
Select the correct scientific notation form of this numeral using only 3 significant figures. 8,468 L
8,468 written in scientific notation is 8.47 x 10³.
What is the scientific notation?Scientific notation is used to compress large numbers in smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
For example:
• The number : 1 x 10² is equivalent to 100
• The number 1 x 10³ is equivalent to 1000
8,468 becomes 8.47 x 10³
To learn more about scientific notation, please check: https://brainly.com/question/25334755
#SPJ1
33-2[3(3+12)-(5x2)3]
Answer:
3
Step-by-step explanation:
33 - 2[3(3 + 12) - (5 x 2)3] =
= 33 - 2[3(15) - (10)3]
= 33 - 2[45 - 30]
= 33 - 2[15]
= 33 - 30
= 3
A t-shirt vendor sells yellow shirts and blue shirts at a ratio of 1:4 what percent of the shirts are yellow?
Answer: 25%
Step-by-step explanation:
Find the weighted average of these values.
Value Weight
7.00 75.0%
8.00 15.0%
9.00 10.0%
By using the concept of weighted averages, the weighted average of the given values is equal to 7.35.
How to determine weighted averages?
Weighted average is a kind of average in which each element has an specific weight in contrast with uniform average, where each element has the same weight. In this problem we have three values associated to three distinct weights, whose weighted average is:
x = 0.75 · 7 + 0.15 · 8 + 0.10 · 9
x = 7.35
By using the concept of weighted averages, the weighted average of the given values is equal to 7.35.
To learn more on weighted averages: https://brainly.com/question/18554478
#SPJ1
6 is added to the product of 7 and a number.
Answer:
7x+6
Product means multiplication
and we'll use X for "number"
and add 6
so 7x+6
The required equation model as of the given condition is 6 + 7×x.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division.
Here,
Let the number be x,
6 is added to the product of 7 and a number.
= 6 + 7 × x
Thus, the required equation model as of the given condition is 6 + 7 × x.
Learn more about models here:
https://brainly.com/question/22591166
#SPJ2
Select the correct answer.
A diagram of angles 1, 2, and 3 Is shown.
Given: Angles 1 and 2 are complementary
m/1=36°
21 and 22 are
complementary
given
m21-36
given
36⁰+ m2 = 90°
definition of
complementary
angles
22 and 23 are
a linear pair
m22+ m23 = 180°
given
linear pairs theorem
What is most likely being shown by the proof?
OA m/1 + m/3 = 90°
OB. m/3 144°
OC m/1 + m/3= 180°
OD. m/3= 126°
m22=54"
subtraction
property of
equality
54+ m23=180"
substitution
property of
equality
Analyzing the given data, it cab be concluded that Option D, that is, mL3 = 126° is most likely being shown by the proof.
It can be observed from the given diagram, angle 1 and angle 2 are complementary. By the definition of complementary angles, we get the sum of angle 1 and angle 2 equal to 90°.
=> mL1 + mL2 = 90°
The value of angle 1 is given as 36.
=> mL1 = 36⁰
Using the first observed condition and the value of angle 1, we can obtain the value of angle 2.
=> 36⁰ + mL2 = 90°
=> mL2 = 90 - 36 = 54°
Therefore, the value of angle 2 is obtained as 54°.
From the diagram given in the question, it can also be inferred that angle 2 and angle 3 form a linear pair. Using the linear pair theorem, we get the sum of angle 2 and angle 3 as 180°.
=> mL2 + mL3 = 180°
Previously, we have obtained the value of angle 2 as 54°.
Hence, by substituting the value of angle 2 in the above equation, we get,
54° + mL3 = 180°
=> mL3 = 180 - 54 = 126°
Therefore, By researching all the data and the results, we can conclude that all other options are discarded and the correct option is option D.
Learn more about Complementary Angles here:
https://brainly.com/question/5708372?referrer=searchResults
#SPJ9
find the coordinates of the points that are 17 units away from the origin and have a y-coordinate equal to −
smaller x value (x, y)=(-15,-8)
larger x value (x, y)=(+15,-8)
[tex]\sqrt{x^{2} + y^{2} } = 17[/tex]
[tex]x^{2} +y^{2} = 289[/tex]
y= -8
[tex]x^{2} =289-64[/tex]
[tex]x^{2} =225[/tex]
x= ±15
The points are (15, -8) and (-15, -8)
What do you mean by coordinates?Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ). Mathematics, scientists, and engineers frequently employ a variety of coordinate systems. The positions of points in 2D or 3D are defined by two or three straight-line axes known as cartesian coordinates, sometimes known as rectangular coordinates. All scales are linear, which means that they are all graduated in uniform-sized increments. The positions of points in 2D are defined by a different coordinate system called semilog coordinates. The other scale is logarithmic while the first is linear.
To learn more about coordinates, Visit:
https://brainly.com/question/26494959
#SPJ4
according to a report on sleep deprivation by the centers for disease control and prevention, the proportion of california residents who reported insufficient rest or sleep during each of the preceding 30 days is 8.0%, while this proportion is 8.8% for oregon residents. these data are based on simple random samples of 11,545 california and 4,691 oregon residents.
[tex]Let$p_1$ - true proportion of California residents who reported insufficient rest or sleep during the preceding 30 days$p_2$ - true proportion of Oregon residents who reported insufficient rest or sleep during the preceding 30 days$\hat{p}_1$ - sample proportion of California residents who reported insufficient rest or sleep during the preceding 30 days $=0.08$$\hat{q}_1=1-\hat{p}_1=1-0.08=0.92$$n_1$ - sample size of CA residents $=11,545$[/tex][tex]$\hat{p}_2$ - sample proportion of Oregon residents who reported insufficient rest or sleep during the preceding 30 days $=0.088$$\hat{q}_2=1-\hat{p}_2=1-0.088=0.912$$n_2$ - sample size of OR residents $=4,691$The $95 \%$ Confidence Interval for $\left(p_1-p_2\right)$ is given by,$$[/tex][tex]\left(\hat{p}_1-\hat{p}_2\right) \pm Z^* \sqrt{\frac{p_1 q_1}{n_1}+\frac{p_2 q_2}{n_2}}$$if $p_1$ and $p_2$ are unknown we use$$\left(\hat{p}_1-\hat{p}_2\right) \pm Z^* \sqrt{\frac{\hat{p}_1 \hat{q}_1}{n_1}+\frac{\hat{p}_2 \hat{q}_2}{n_2}}$$where $Z^*=Z_{\frac{\alpha}{2}}=Z_{0.0250}$[/tex][tex]Plugging in, we get$$\begin{aligned}\left(\hat{p}_1-\hat{p}_2\right) \pm Z^* \sqrt{\frac{\hat{p}_1 \hat{q}_1}{n_1}+\frac{\hat{p}_2 \hat{q}_2}{n_2}} \\(0.08-0.088) & \pm 1.96 \sqrt{\frac{0.08(0.92)}{11545}+\frac{0.088(0.912)}{4691}} \\&-0.008 \pm 0.009498026 \\&(-0.017498026,0.001498026) \\& \approx(-0.0175,0.0015)\end{aligned}$$[/tex][tex]a) For the Hypothesis Test we have,- i) State the hypotheses.$$\begin{aligned}&H_0: p_1-p_2=0 \\&H_1: p_1-p_2 \neq 0\end{aligned}$$[/tex]
What is hypothesis?A hypothesis test examines a suggested mathematical model to see if a sample of data contains enough evidence to disprove the null hypothesis.
To know more about hypothesis, visit;
https://brainly.com/question/13025783
#SPJ4
What is an equation of the line that passes through the point (4,−3) and is parallel to the line x-2y=2?
Answer:
y = 1/2x - 5
or x - 2y = 10
Step-by-step explanation:
x - 2y = 2
2y = x - 2
y = 1/2x - 1
If two lines are parallel, their slopes are equal
so m = 1/2, y = -3, x = 4
y = mx + b
-3 = 1/2(4) + b
-3 = 2 + b
b = -5
so y = 1/2x - 5
or 2y = x - 10
x - 2y = 10
Write the standard equation for each ellipse.
25x^2+9y^2+100x+18y=116
The standard equation of each ellipse is ( 2,1)
Let a=x^2
b=y^2
And 2h=xy coefficient of term
Then the second degree equation represent an ellips hyperbola as
ab-h^2>= or <0
Here ab-h^2=225>0
The equation can be written as
(x+2)^2/9+(y-1)^2/25=1
Center c of the elips is (-2,1)
A
a=5
b=3
axis x=-2
e=✓a^2-5^2/5
=2✓14/5
As
S=S`
Cs=Cs`=✓14
ellipse=(2,1+√14) (2,1,√-14)
To know about ellipse click
https://brainly.com/question/16160944
#SPJ9
what is the answer i don’t understand how to do this i’m stuck please help asap i missed a week of school can you help me please? it’s very important please help
Answer:
Please see the picture below.
Step-by-step explanation:
Please help me with this geometry question. x and pr needed ao basically like this x=(answer), PR=(answer). Thank you
Answer:
x = -1, PR = 38.
Step-by-step explanation:
As Q is the midpoint of PR
PQ = QR
6x + 25 = 16 - 3x
9x = -9
x = -1.
PR
= 6x + 25 + 16 - 3x
= 6(-1) + 25 + 16 - 3(-1)
= -6 + 25 + 16 + 3
= 38.
Please Perform The Operation.
Add:
1.) A - 5
+ 2a - 3
2.) 5t² - 6st + 8t - 3
+ 7t² + 8st - 2t + 9
3t² + 2st + 5t + 5
Subtract:
1.) 10m - 2n - 1
- 5m - 2n + 2
2.) -5x³ + 3x² +6x
- 3x³ + 9x² + 4x
:)
The resulting polynomials are listed below:
3 · a - 8 15 · t² + 4 · s · t + 11 · t + 11 5 · m - 3 - 8 · x³ + 12 · x² + 10 · xWhat are the resulting expression by adding and subtracting polynomials?Herein we find two cases of addition of polynomials and the two cases of subtraction of polynomials. Each operation must be done by taking algebra properties into account. Complete procedures are shown below:
Addition - Case 1
(a - 5) + (2 · a - 3) Given
(a + 2 · a) + [- 5 + (- 3)] Associative and commutative properties
3 · a - 8 Distributive property / Definitions of addition and subtraction
Addition - Case 2
(5 · t² - 6 · s · t + 8 · t - 3) + (7 · t² + 8 · s · t - 2 · t + 9) + (3 · t² + 2 · s · t + 5 · t + 5) Given
(5 · t² + 7 · t² + 3 · t²) + (- 6 · s · t + 8 · s · t + 2 · s · t) + (8 · t - 2 · t + 5 · t) + (- 3 + 9 + 5) Associative and commutative properties
15 · t² + 4 · s · t + 11 · t + 11 Distributive properties / Definitions of addition and subtraction / Result
Subtraction - Case 1
(10 · m - 2 · n - 1) - (5 · m - 2 · n + 2) Given
(10 · m - 5 · m) + (- 2 · n + 2 · n) + (- 1 - 2) Commutative and associative properties / (- a) · (- b) = a · b / (- a) · b = - a · b
5 · m - 3 Distributive property / Cancellative property / Definition of addition and subtraction / Modulative property / Result
Subtraction - Case 2
(- 5 · x³ + 3 · x² + 6 · x) - (3 · x³ + 9 · x² + 4 · x) Given
(- 5 · x³ - 3 · x³) + (3 · x² + 9 · x²) + ( 6 · x + 4 · x) Commutative and associative properties / (- a) · (- b) = a · b / (- a) · b = - a · b
- 8 · x³ + 12 · x² + 10 · x Distributive property / Definition of addition and subtraction / Result
To learn more on polynomials: https://brainly.com/question/11536910
#SPJ1
flip 98 fair coins and 1 hh coin and 1 tt coin. given that you see an h, what is the probability that it was the hh coin? explain in layman’s terms.
The probability that it was an HH coin is [tex]\frac{1}{50}[/tex]
Conditional Probability P(B/A) is defined as probability of occurrence of B given that A has already occurred .
Baye's Theorem describes the probability of an event based on conditions that might be related to event .
P(A/B)={P(B/A)*P(A)}/P(B)
Total number of coins =100
Total number of HH coins = 1
P(HH) =Probability of getting HH=1/100
P(H/HH)=Probability of H knowing that HH has already occurred=1
Next to find Probability Of H
We need to find two thing
(i) Probability H appears and is a fair coin= [tex]\frac{1}{2} *\frac{98}{100} =\frac{98}{200}[/tex]
(ii)Probability H appears and is a HH coin = [tex]\frac{1}{100}[/tex]
P(H)= (i)+(ii) =100/200=1/2
BY Baye's Theorem
P(HH|H)={P(H|HH)∗P(HH)}/P(H)
[tex]=\frac{1*\frac{1}{100} }{\frac{100}{200} }[/tex]
[tex]=\frac{2}{100}[/tex]
[tex]=\frac{1}{50}[/tex]
Therefore , The probability that it was an HH coin is [tex]\frac{1}{50}[/tex]
Learn more about Probability https://brainly.com/question/26865314
#SPJ4
Reduce completely
[tex]1*2*3*4*5*6\\--------\\6*7*8*9*10[/tex]
f(x) = x; vertical stretch by a factor of 2 followed by a translation 1 unit up
Answer:
f(x)=2x+1
Step-by-step explanation:
Use formula:
f(x)=a(x-h)+k
a=shrinking/stretching
h= horizontal translation
left (+)
right (-)
k= vertical translation
left (-)
right (+)
How is the graph of g(x) = -(2x)³ related to
the graph of f(x) = x³ ?
The graph of g(x) is a vertical compression of
the graph of f(x) by a factor of 2 and a reflection
across the x-axis.
The graph of g(x) is a horizontal compression of
1
the graph of f(x) by a factor of 2 and a reflection
across the x-axis.
The graph of g(x) is a horizontal stretch of the
graph of f(x) by a factor of 2 and a reflection
across the y-axis.
pls help no wrong answers will report
Select the correct answer from each drop-down menu.
Consider the equation below.
The equation was solved using the following steps.
Step 1:
Step 2:
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Complete the statements below with the process used to achieve steps 1-4.
Step 3:
Step 4:
-2(5z + 8) = 14 + 6x
-2 to 5x and 8.
6x.
16.
-16.
-10 16 = 14 + 6x
-162 16 = 14
-16z
30
-
H
11
11
11
- 15
For solve the equation there are following prpperties are used
Step -1 Distributive properties,
Step - 2 Subtraction,
Step - 3 Addition, and
Step - 4 Division.
The distributive property of multiplication , simplify expressions wherein multiply a number by a sum or difference. According to this property, the product of a sum or difference of a number is equal to the sum or difference of the products.
Given equation -
-2(5x + 8) = 14 + 6x
The equation was solved using the following steps.
Step 1: -10x - 16 = 14 + 6x
Step 2: -10x - 6x - 16 = 14 = -16x -16 = 14
Step 3: -16x = 30
Step 4: x = -30 / 16
Step 5: x = -15/8.
Complete the statements with the process used to achieve steps 1-4.
Step 1 - here we are using distributive properties
-10x -16 = 14 + 6x
distribute -2 in the parenthesis to 5x and 8
Step 2 - by subtraction method
-16x - 16 = 14
subtraction of -6x
Step 3 - Aply addition
-16x = 30
Addition of 16
Step 4 - Division
x = -30/16
division of -16
x = -15 / 8
Hence , Step- 1, 2, 3, and 4 are distributive properties, subtraction, addition, and division respectively.
Learn more about distributive properties
visit - https://brainly.com/question/2807928
#SPJ9
Par un beau dimanche ensoleilé Julien se promene
Answer:
watashiwa ana men toire ne duse ka
fipinjin desu
fraction equivalent to 4/6 with 3 as denominator
Answer:
2/3
Step-by-step explanation:
6 divided by 3 is 2, so you have to divided 4 by 2, which is 2.
Answer:
⅔
Step-by-step explanation:
4 divide by 2 = 2
6 3
therefor 2/3 is equvelet too 4/6.
Hope this helped
What is the measure of angle B if angle C is 34 degrees and angle A is unknown?
Answer:
The measure of B is 56 degrees.
Write the equation of the parabola in vertex form.
vertex (3,4), point (1,-4)
Answer:
y = - 2(x - 3)² + 4
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here (h, k ) = (3, 4 ) , then
y = a(x - 3)² + 4
to find a substitute (1, - 4 ) into the equation
- 4 = a(1 - 3)² + 4 ( subtract 4 from both sides )
- 8 = a(- 2)² = 4a ( divide both sides by 4 )
- 2 = a
y = - 2(x - 3)² + 4 ← equation in vertex form
jackie has a checking account. For each day that her checking account balance falls below zero, she is charged by the bank a fee of $7.50 per day. Her current balance in the account is –$12.50. If she does not make any deposits or withdrawals, what will be the new balance in her account after 2 days? Show your work.
The new balance in Jackie's account after 2 days will be -$27.50.
How to illustrate the expression?It should be noted that for each day that her checking account balance falls below zero, she is charged by the bank a fee of $7.50 per day.
Since her current balance in the account is –$12.50, the new balance after 2 days will be:
= -12.50 + (-7.50 × 2)
= -12.50 + -15
= -27.50
The balance is -27.50
Learn more about checking account on:
brainly.com/question/26181559
#SPJ1
The point D is the midpoint of a segment CF. CF = 2y-2 and CD = 3y - 11. a) find y b) find CD
The value of y = 5 and CD = 4 cm in the segment.
What is a segment ?The point D is the midpoint of a segment CF. CF = 2y-2 and CD = 3y - 11.
CD = (1/2) CF
3y - 11 = (1/2) (2y -2) (multiply both sides by 2)
6y - 22 = 2y - 2
6y - 2y = -2 + 22
4y = 20
y = 5
Substitute with the value of y in the equation of CD, you get:
CD = 3y-11 = 3(5) - 11 = 15 - 11 = 4 cm
In geometric terms, a line segment is a section of a straight line that is bordered by two clearly defined end points and contains all of the points on the line that lie inside that segment. The Euclidean distance between two endpoints of a line segment provides the length of the segment.
Between two points of a line or curve. a portion of a plane or solid figure that is eliminated due to the intersection of a line, plane, or planes, particularly one that occurs between a chord and a circle's arc.
A line segment in geometry is bordered by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points.
To learn more about segment from the given link:
brainly.com/question/12728072
#SPJ9
what is this equation 6+4÷2
Answer:
Step-by-step explanation:
6+4=10
10/2
answer =5
The craft teacher has 12 sheets of blue chart paper and 18 sheets of red chart paper. How many equal piles of chart paper can she make such that each pile has only one color?
The equal piles of chart paper that she can make such that each pile has only one color is 6.
How to illustrate the information?It should be noted that from the information, the craft teacher has 12 sheets of blue chart paper and 18 sheets of red chart paper.
In this case, the highest common factor between the numbers is 6
Therefore, the piles of chart paper that she can make such that each pile has only one color is 6.
Learn more about color on:
brainly.com/question/911645
#SPJ1
Thomas has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. For each part below, if the marble selected is replaced before the next marble is drawn, find the probability for the given draw. Write your answer as a simplified fraction.
A.What is the probability of getting a red marble?
B.What is the probability of getting a red or a green marble?
C.What is the probability of getting an orange marble?
Using it's concept, the probabilities are given as follows:
A. 1/4.
B. 11/16.
C. 0.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, the number of marbles is given by:
7 + 5 + 4 = 16.
Then:
For item a, 4 are red, hence the probability is 4/16 = 1/4.For item b, 4 are red and 7 are green, hence the probability is 11/16.For item c, there are no orange marbles, hence the probability is of 0.More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ1
You have 16 digs for your current volleyball season. There are 3 games left in the season. You want to break your previous record of 20 digs in a
season. Write and solve an inequality that represents the number 2 of digs you must get in the remaining 3 games to break your record
Answer: 16+d>20
d>4
Step-by-step explanation:
d=digs
16+d>20
16-16+d>20-16
d>4