The function is an exponential function; the initial value is -6.1 and the base is 3
How to determine the function type?The equation of the function is given as:
y = -6.1 *(3^x)
An exponential function is represented as:
y = ab^x
Where:
Initial value = a
base = b
By comparison, we have
a = -6.1 and b = 3
Hence, the function is an exponential function; the initial value is -6.1 and the base is 3
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Dollar General sold garden hoses at a reduced price of $7.64 and took an end of the season markdown of $12.35. What was the original selling price of each hose? Use formula M=S-N = selling price-reduced price
The original selling price of the garden hoses is $19.99
How to find the original selling price?Using the given formula,
M = S - N
where
M = markdownS = original selling price,N = reduced priceHence,
M = $12.35.
N = $7.64
Therefore,
S = M + N
S = 12.35 + 7.64
S = $19.99
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Solve for x in the diagram below.
Answer:
X = 15
Step-by-step explanation:
We can tell that the two sides that show the degrees are equal because of the arc. We can set up a simple equation:
x + 45 = 60
x = 15
Answer:
x = 15°
Explanation:
The two marked angles are equal as they are vertically opposite angles.
∴ x + 45° = 60°
⇒ x = 60° - 45°
⇒ x = 15°
identify the asymptotes and state the end behavior of the function f(x)=5x/x-25
Using it's concepts, it is found that for the function [tex]f(x) = \frac{5x}{x - 25}[/tex]:
The vertical asymptote of the function is x = 25.The horizontal asymptote is y = 5. Hence the end behavior is that [tex]y \rightarrow 5[/tex] when [tex]x \rightarrow \infty[/tex].What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity. They also give the end behavior of a function.In this problem, the function is:
[tex]f(x) = \frac{5x}{x - 25}[/tex]
For the vertical asymptote, it is given by:
x - 25 = 0 -> x = 25.
The horizontal asymptote is given by:
[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{5x}{x - 25} = \lim_{x \rightarrow \infty} \frac{5x}{x} = 5[/tex]
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2.5 pts Each week 5 new office phones are installed in a major network company. At the beginning of March, 200 phones had already been installed. Write a linear equation to model this situation. Do not use spaces in the equation.
Use your equation if the company wanted to replace all phones in the building (500 total). How many weeks would it take to finish this project?
The linear equation formed is y = 200 +5x and 60 weeks will be required to finish the project.
What is an Equation ?A statement that relates two mathematical expressions by an equal sign is called an Equation.
It is given that
No. of phones Per week installed in the office = 5
Let the no. of phones installed at the present week is given by y
and let x weeks have passed by before that
then the linear equation is formed as
y = 200 +5x
If the company wants to replace all the phones
Total phones = 500
No. of week required = ?
500 = 200+5x
300 = 5x
x = 60
Therefore 60 weeks will be required to finish the project.
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Northlake High School has two lunch periods. Students can eat their lunch in
the cafeteria or on an outside patio. About 35% of students who have first
lunch eat outside. Compare this with the percentage of second-lunch
students who eat outside.
First lunch
Second lunch
Total
Select the true statement.
Eat outside
0.19
0.18
0.41
Eat inside
0.35
0.24
0.59
Total
0.54
0.46
1.0
Based on the given information on the first and second lunch students, the true statement is B. A greater percentage of second-lunch students (39%) eat outside.
which lunch students eat more outside?the percentage of second lunch students who eat their lunch outside is:
= Second lunch students who eat outside / Second lunch students
this gives:
= 0.18 / 0.46 x 100%
= 39%
options for this question include:
A. A smaller percentage of second-lunch students (24%) eat outside.
B. A greater percentage of second-lunch students (39%) eat outside.
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Susan begins counting backward from 1298 by 4's, saying one number every 5 seconds. At the same time, Jim begins counting forward from 171 by 3's, saying one number every 5
seconds. What number will they both say at the same time? (By the way I'm only in 6th grade so please explain well :)
Answer:
Step-by-step explanation:
Whats the correct answer answer asap
The environmental threat in Japan and Korea that threatens food security is: B. soil erosion.
What is Soil Erosion?Soil erosion can be defined as the washing away of the top soil that supports plants growth and also contains vital nutrients for plants growth.
Crops are grown majorly on land. The disruption of soil nutrients by soil erosion poses a serious environmental threat to food security in both Japan and Korea. Therefore, the answer is: B. soil erosion.
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A nut store normally sells cashews for $4.00 per pound and peanuts for $1.50 per pound. But at the end of the month the peanuts had not sold well, so, in order to sell 10 pounds of peanuts, the manager decided to mix the 10 pounds of peanuts with some cashews and sell the mixture for $3.50 per pound. How many pounds of cashews should be mixed with the peanuts to ensure no change in the revenue?
If you bought 20 pounds of cashews, your bottom line would remain the same.
How many pounds of cashews should be mixed with the peanuts to ensure no change in the revenue?Cashew and peanut butter together represent a linear relationship. Twenty pounds of cashews would have no impact on profits.
Cashews are represented here by the letter c and peanuts by the letter p.
U-4.00
Up=1.50
Um=2.00
p-40 pounds of peanuts that have not been sold.
m=40+c -when 40 pounds of peanuts are combined with cashews, the resulting combination
Generally, the equation for c is mathematically given as
Ue x c+Up xp=Um x m
Therefore
4.00 x c+1.50 x 40 2.00 x (40+c)
4c+60-80+2c
2c= 20
c=10
In conclusion, If you bought 20 pounds of cashews, your bottom line would remain the same.
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Calculate the slope of the line between the pairs of points in each of the tables to determine which table represents a linear function.
Answer:
B
Step-by-step explanation:
Hope it helps :)
Daphne and Josephine earn commission on the sales they each make. Daphne earned $80 in commission on a sale of $1,600 . Josephine earn: twice the commission percentage as Daphne. If the commission Josephine earns is $150 , how much were her sales, in dollars?
Josephine's sales in dollar is $1500.
What is Josephine's sales in dollars?The first step is to determine the percentage commission earned by Daphne.
Percentage commission : ($80 / $1600) x 100 = 5%
Percentage commission of Josephine: 5% x 2 = 10%
Josephine's sales = dollar commission / percentage commission
$150 / 0.1 = $1500
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Suppose $24,000 is deposited into an account paying 7.25% interest, which is compounded continuously.
How much money will be in the account after ten years if no withdrawals or additional deposits are made?
$49,553.54
$48,326.40
$47,897.10
$46,414.20
Answer:
$49,553.54
Explanation:
[tex]\sf Continuously \ compound \ interest : {A = P e^{rt}[/tex]
[tex][\sf where \ A \ is \ final \ amount, \ P \ is \ principal \ amount, \ r \ is \ interest \ rate, \ n \ is \ years][/tex]
Here given following:
principal amount (P) = $24,000rate of interest (r) = 7.25%years (t) = 10 yearsInserting these values in formula:
[tex]\rightarrow {A = 24000e^{7.25\% (10)}[/tex]
simplify following
[tex]\rightarrow {A = 49553.54[/tex]
Katelyn was asked to solve for the unknown the problem shows that n +6=13 her steps are shown below
The solution of the unknown equation n + 6 = 13 will be n = 7.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1.
The standard form of a linear equation is of the form Ax + B = 0.
The given equation is
n +6=13
To solve for n
Subtract 6 on both sides;
n +6=13
n = 13- 6
n = 7
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What is the quadratic regression equation that fits these data?
X
-4
-3
-2
-1
0
1
2
3
4
O A. ý = 0.82x2 + 0.78x+7.23
OB. 9=1642 +1.24x+8.08
O c. y = 2.13x² +0.13x+ 6.39
O D. = 16.76 1.02*
40
28
10
8
7
10
16
26
40
Using a calculator, the quadratic regression equation that fits the data is:
C. y = 2.13x² + 0.13x + 6.39
How to find the equation of regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
In this problem, the points are:
(-4,40), (-3,28), (-2, 10), (-1, 8), (0,7), (1,10), (2,16), (3,26), (4,40).
Hence the equation is:
C. y = 2.13x² + 0.13x + 6.39
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Does anyone know how to do this please help
18 + 5 + 23=46
Step-by-step explanation:
Answer:
1238
Step-by-step explanation:
Find the value of y.
A. 4
B. 6
C. 10
D. 12
Answer:
y=12
Step-by-step explanation:
30,60,90 triangle
8*rad3=8rad3
8rad3/2=4rad3
4rad3*rad3=12
Which expression is equivalent to (43) (
what is the following product?
(2√7 + 3√6) (5√5 +4√3)?
22, 66, 198, ...
Find the 8th term.
Answer:
The 8th term will be 48114.
Step-by-step explanation:
This series is an geometric series.
The formula for the nth term in an geometric series is [tex]ar^{n-1}[/tex], where a is the first term, r is the ratio (how much each term is multiplied by and n is the term you want to find.
In this question, the 8th term will be [tex]22\times3^7[/tex] = 48114
you randomly select one card from a 52 card deck find the probability of selecting a ace or a two
In 2000, the total population of the U.S. was 281.4 million people. In 2010, it was 308.7 million people. What is the average rate of change in the total population over this time period?
2.73 million people per year
27.3 million people per year
13.6 million people per year
1.36 million people per year
Answer:
2.73 million people per year
Step-by-step explanation:
Turn sentences into coordinates/points:
In 2000, 281.4 million people
(x₁, y₁) = (2000, 281.4)In 2010, 308.7 million people
(x₂, y₂) = (2010, 308.7)Rate of population per year:
[tex]\sf \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf \dfrac{308.7-281.4}{2010-2000}[/tex]
[tex]\rightarrow \sf 2.73 \ million \ people[/tex]
monthly payments of $75 are paid into an annuity beginning on January 31, with a yearly interest rate of 3%, compounded monthly. Add the future values of each payment to calculate the total value of the annuity on september 1.
The annuity on September 1 will be $621.43 if the monthly payments of $75 are paid into an annuity beginning on January 31, with a yearly interest rate of 3%
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
We have:
Monthly payments of $75 are paid into an annuity beginning on January 31, with a yearly interest rate of 3%.
Value of annuity as of September 1 calculation:
From the table:
For Jan:
Jan 0 $75.00 1.07214 $80.41
For Feb
Feb 1 $75.00 1.06152 $79.61
And on September 1, the value of the annuity will be: =
= $621.43
Thus, the annuity on September 1 will be $621.43 if the monthly payments of $75 are paid into an annuity beginning on January 31, with a yearly interest rate of 3%
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Please answer all parts as I know the answers but need the work to go with them. Thus, I believe the above answers are correct. Thank you!
As the sample size n is less than 30 normal distribution is used.
The values of x are converted into z by using the formula z= x-u/ s and then the z values are found out from the table.
The limits are found by using the formula x±σz or x±sz where s= σ
As the sample size is 10 which is less than 30 the normal distribution is used.
The probability of x< 2.59 is 0.3446
The probability 2.60<X <2.63 is 0.9484
So lower and upper limits are 2.607 and 2.612
Part A
As the sample size is 10 which is less than 30 the normal distribution is used.
Part B
For given value of x= 2.59 z is obtained =0.4
x= 2.59
z= x-u/ s
z= 2.59-2.61/0.05
z= -0.02/0.05
z=- 0.4
P (X<2.59) = P(-0.4 <Z<0) = 0.5 -0.1554= 0.3446
The probability of x< 2.59 is 0.3446
Part C
For two given values of x= 2.60 and 2.63 z is obtained as =0.2 and 0.4
x1= 2.60
z1= x-u/ s
z= 2.60-2.61/0.05
z= -0.01/0.05
z=- 0.2
x2= 2.63
z2= x-u/ s
z= 2.63-2.61/0.05
z= 0.02/0.05
z= 0.4
P (2.60<X<2.63) = P(-0.2 <Z<0.4)
= P(-0.2 <Z<0)+ P(0 <Z<0.4)
=0.793 + 0.1554= 0.9484
The probability 2.60<X <2.63 is 0.9484
Part D"
p= 0.57
From the table z= 0.045
z= x-u/ s
zs= x-u
zs+u = x
x1= 0.045*0.05 +2.61= 2.61225
x2= 2.61- 0.00225= 2.60775
So lower and upper limits are 2.607 and 2.612
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does anyone know how to solve this?
Just put -2 in,where X is and get your answer that way
Select the correct answer. Suppose that 3 boys and 2 girls go to the theatre and occupy 5 seats in a row. In how many ways can they be seated if all 3 boys sit together?
Answer:
Possibly 3
Step-by-step explanation:
Lets say
g=girls
b=boys
1st option: gbbbg
2nd option: bbbgg
3rd option: ggbbb
let A and B sets. when do we say set A is equal to set B
Answer:
We say sets A and B are equal, and write A = B if they have exactly the same elements.
Step-by-step explanation:
Answer:
When set A is equal to set B. It is denoted as A = B.
Have a nice day!
Ramona Oden deposited $6,000 at 5.5% interest compounded daily for 25 days.
Find the a) amount, and b) compound interest
The table shows the size of outdoor decks (x) in square feet, and the estimated dollar cost to construct them (y).
y
xy
100
600
10,000
60,000
144
850
20,736
122,400
225
1,300
50,625
292,500
324
1,900
104,976
615,600
400
2,300
160,000
920,000
Σχ=1,193 | Σy=6,950 | Ex?=346,337 | Σxy=2,010,500
Which regression equation correctly models the data?
X
xy=5.83x-1.04
y = 5.83x + 17
y = 5.71x + 29
y
= 5.71x + 27.6
Submitted
The regression equation of the table is y = 5.71x + 27.6
How to estimate the regression equation?From the table of values, we have the following parameters:
[tex]\sum x = 1193[/tex]
[tex]\sum y = 6950[/tex]
[tex]\sum x^2 = 346337[/tex]
[tex]\sum xy = 2010500[/tex]
Calculate A using
[tex]A = \frac{\sum y * \sum x^2 - \sum x * \sum xy}{n\sum x^2 - (\sum x)^2}[/tex]
This gives
[tex]A = \frac{6950 * 346337 - 1193 * 2010500}{5 * 346337 - (1193)^2}[/tex]
Evaluate
[tex]A = \frac{8515650}{308436}[/tex]
Divide
A = 27.6
Calculate B using
[tex]B = \frac{n\sum xy - \sum x * \sum y}{n\sum x^2 - (\sum x)^2}[/tex]
This gives
[tex]B = \frac{5 * 2010500 - 1193 * 6950}{5 * 346337 - (1193)^2}[/tex]
Evaluate
[tex]B = \frac{1761150}{308436}[/tex]
Divide
B = 5.71
The regression equation is represented as:
y = Bx + A
So, we have
y = 5.71x + 27.6
Hence, the regression equation of the table is y = 5.71x + 27.6
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Solve the system of equations. Type in all points of intersection for the two functions and round to the nearest tenth if necessary f(x)=sr5x+25-1 g(x)=x^2-2x-3
The solution to the system of equations are (-1.7, 3.1) and (4.1, 5.8)
How to solve the system of equation?The equations are given as:
[tex]f(x)=\sqrt{5x+25}-1[/tex]
[tex]g(x)=x^2-2x-3[/tex]
Next, we plot the graph of the equations (see attachment)
From the attached graph, we can see that both equations intersect at (-1.7, 3.1) and (4.1, 5.8)
Hence, the solution to the system of equations are (-1.7, 3.1) and (4.1, 5.8)
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If p = the price of a pair of basketball shoes, which algebraic expression
represents the phrase below?
4
the difference of the price of the shoes and 5 dollars
A. 5p
B. p+5
c. ff
D. p-5
Hello :
The difference of the price of the shoes and 5 dollars is p - 5.
find the midpoint of the segment with endpoints at (-2,1) and (0,9) using (x1+x2,y1+y2)
Answer:
(-1, 5)
Step-by-step explanation:
Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]
Define the endpoints:
[tex]\textsf{let}\:(x_1,y_1)=(-2,1)[/tex][tex]\textsf{let}\:(x_2,y_2)=(0,9)[/tex]Substitute the defined points into the formula:
[tex]\begin{aligned}\implies \textsf{Midpoint} & =\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\\\\ & =\left(\dfrac{0+(-2)}{2},\dfrac{9+1}{2}\right)\\\\& =\left(\dfrac{-2}{2},\dfrac{10}{2}\right)\\\\& =\left(-1,5\right)\end{aligned}[/tex]
Therefore, the midpoint of the segment with endpoints (-2, 1) and (0, 9) is (-1, 5).
2. In factored form, a quadratic function can be written as y = (-2-x) (x-8). This parabola goes through the points (-2, 0) and (8, 0). Use your knowledge of the symmetry of the parabola to find the vertex. Show all work. 4 mark
Answer:
(3, 25)
Step-by-step explanation:
The symmetry of a parabola means that if you have two y coordinates which are the same, the axis of symmetry is going to be in the middle of the x-coordinates. So in this case it's the middle number of -2 and 8. So to find the midpoint of these two numbers, you simply add them together and divide it by 2. This gives you the equation: [tex]\frac{-2+8}{2}=\frac{6}{2}=3[/tex]. This means that the axis of symmetry is at: [tex]x=3[/tex], and as you may know, this axis of symmetry passes through the vertex. So this means the x-axis of the vertex is 3, so to find the y-value simply plug in 3 as x
y = (-2-3)(3-8)
y = (-5)(-5)
y = 25
So this means the vertex is at (3, 25)