A store gives customers a markup of 13%. If the store sells a belt for $25, what was the wholesale price paid for the belt by the store?
Answer:
$22.12
Step-by-step explanation:
Let x be the wholesale price (the price before adding the markup).
The markup is 13%, so 13% of x is added to x.
x + 13%x = $25
x + 0.13x = 25
1.13x = 25
x = 25/1.13
x = 22.12
(1 point) Find a formula for the nth term in the sequence: 17,−17/8,17/27,−17/64,17/125,…
Given:
The sequence is:
[tex]17,-\dfrac{17}{8},\dfrac{17}{27},-\dfrac{17}{64},\dfrac{17}{125},...[/tex]
To find:
The formula for the nth term in the given sequence.
Solution:
We have,
[tex]17,-\dfrac{17}{8},\dfrac{17}{27},-\dfrac{17}{64},\dfrac{17}{125},...[/tex]
The given sequence can be written as
[tex]\dfrac{17}{1^3},-\dfrac{17}{2^3},\dfrac{17}{3^3},-\dfrac{17}{4^3},\dfrac{17}{5^3},...[/tex]
The sign are alternative and the absolute value of each term can be defined by the expression [tex]\dfrac{17}{n^3}[/tex], where n is a natural number.
So, the required formula is:
[tex]a_n=(-1)^{n+1}\dfrac{17}{n^3}[/tex]
Therefore, the formula for nth term in the given sequence is [tex]a_n=(-1)^{n+1}\dfrac{17}{n^3}[/tex].
c) Share £160 in the ratio 1:9
(2)
Answer £
and £
Answer:
£16:£144
Step-by-step explanation:
1+9=10
160/10=16
1×16=16
9×16=£144
Answer:
16£ and 114£
Step-by-step explanation:
add the ratios
1 + 9 = 10
for the first ratio
(1/10) × 160
= 16£
for the second ratio
(9/10) × 160
= 114£
Can you help me, please?
Answer:
The first one is two over four
Step-by-step explanation:
Please help me with this question! and tysm!
Answer:
272
Step-by-step explanation:
u do 68*4 because it said 4 times as henery
Hope this helps
Answer:
272
Step-by-step explanation:
4 times 68 = 272
If someone makes as many slices of toast as possible in 4 minutes and 40 seconds, how many slices do think they can make
Answer:
If they can do x slices per second, they could do 280x slices
Step-by-step explanation:
4 min 40 sec -> 280 secs
280 * 5 = 1400
What is the answer for B
Please help and use the proper theorem!
please help me asap
Answer C
Step-by-step explanation:
show proof and work for brainliest
PLEASE HELP!!
Solve for m
m+7=3+m+4
Answer:
M = -7
Step-by-step explanation:
It makes sense if you replace it in for M! Hope this helps and have a great day!
the 20% tip on a $8 sandwich
Answer:
Tip of $1.60
The total is $9.60
Step-by-step explanation:
(20% × $8) + $8
$1.60 + $8
$9.60
Evaluate the expression: 1/3 (4x3)+2^3.
Write the equation in vertex form. Then identify the vertex, axis of symmetry, and direction of opening.
y = 2x^2 + 2
Step-by-step explanation:
y-2=2(x-0)^2
Vertex: (0,2)
Axis of Symmetry is x=0
Opens upward
Hope that helps :)
Consider the point on the polar graph below.
Represent the point's location in the polar form (r,θ) where 0≤r<50 and 0≤θ<2π.
(r,θ)=
Represent the point's location in the polar form (r,θ) where 0≤r<50and 2π≤θ<4π.
(r,θ)=
Represent the point's location in the polar form (r,θ) where 0≤r<50and −2π≤θ<0.
(r,θ)=
J0IN G00GLE MEET GIRL$
wnp-hxru-ipf
What is the value of the discriminant? 3y2 = 8y + 2
−40
56
72
88
Answer:
88
Step-by-step explanation:
a = 3
b = -8
c = -2
(-8)² 4(3)(-2) = 64 + 24
an exponential function f is defined by f(x)=c^x where c is a constant greater than 1 if f (7) = 4 x f (5) what is the value of c
From the above, it can be seen that the nature of polynomial functions is dependent on its degree. Higher the degree of any polynomial function, then higher is its growth. A function which grows faster than a polynomial function is y = f(x) = ax, where a>1. Thus, for any of the positive integers n the function f (x) is said to grow faster than that of fn(x).
Thus, the exponential function having base greater than 1, i.e., a > 1 is defined as y = f(x) = ax. The domain of exponential function will be the set of entire real numbers R and the range are said to be the set of all the positive real numbers.
It must be noted that exponential function is increasing and the point (0, 1) always lies on the graph of an exponential function. Also, it is very close to zero if the value of x is mostly negative.
Exponential function having base 10 is known as a common exponential function. Consider the following series:
Derivative of logarithmic and exponential function 5
The value of this series lies between 2 & 3. It is represented by e. Keeping e as base the function, we get y = ex, which is a very important function in mathematics known as a natural exponential function.
For a > 1, the logarithm of b to base a is x if ax = b. Thus, loga b = x if ax = b. This function is known as logarithmic function.
Derivative of logarithmic and exponential function 2
For base a = 10, this function is known as common logarithm and for the base a = e, it is known as natural logarithm denoted by ln x. Following are some of the important observations regarding logarithmic functions which have a base a>1.
The domain of log function consists of positive real numbers only, as we cannot interpret the meaning of log functions for negative values.
For the log function, though the domain is only the set of positive real numbers, the range is set of all real values, i.e. R
When we plot the graph of log functions and move from left to right, the functions show increasing behaviour.
The graph of log function never cuts x-axis or y-axis, though it seems to tend towards them.
Derivative of logarithmic and exponential function 3
Logap = α, logbp = β and logba = µ, then aα = p, bβ = p and bµ = a
Logbpq = Logbp + Logbq
Logbpy = ylogbp
Logb (p/q) = logbp – logbq
Exponential Function Derivative
Let us now focus on the derivative of exponential functions.
The derivative of ex with respect to x is ex, i.e. d(ex)/dx = ex
It is noted that the exponential function f(x) =ex has a special property. It means that the derivative of the function is the function itself.
(i.e) f ‘(x) = ex = f(x)
Exponential Series
Exponential Functions
Exponential Function Properties
The exponential graph of a function represents the exponential function properties.
Let us consider the exponential function, y=2x
The graph of function y=2x is shown below. First, the property of the exponential function graph when the base is greater than 1.
Exponential Functions
Exponential Function Graph for y=2x
The graph passes through the point (0,1).
The domain is all real numbers
The range is y>0
The graph is increasing
The graph is asymptotic to the x-axis as x approaches negative infinity
The graph increases without bound as x approaches positive infinity
The graph is continuous
The graph is smooth
Exponential Functions
Exponential Function Graph y=2-x
The graph of function y=2-x is shown above. The properties of the exponential function and its graph when the base is between 0 and 1 are given.
The line passes through the point (0,1)
The domain includes all real numbers
The range is of y>0
It forms a decreasing graph
The line in the graph above is asymptotic to the x-axis as x approaches positive infinity
The line increases without bound as x approaches negative infinity
It is a continuous graph
It forms a smooth graph
Exponential Function Rules
Some important exponential rules are given below:
If a>0, and b>0, the following hold true for all the real numbers x and y:
ax ay = ax+y
ax/ay = ax-y
(ax)y = axy
axbx=(ab)x
(a/b)x= ax/bx
a0=1
a-x= 1/ ax
Exponential Functions Examples
The examples of exponential functions are:
f(x) = 2x
f(x) = 1/ 2x = 2-x
f(x) = 2x+3
f(x) = 0.5x
Solved problem
Question:
Simplify the exponential equation 2x-2x+1
Solution:
Given exponential equation: 2x-2x+1
By using the property: ax ay = ax+y
Hence, 2x+1 can be written as 2x. 2
Thus the given equation is written as:
2x-2x+1 =2x-2x. 2
Now, factor out the term 2x
2x-2x+1 =2x-2x. 2 = 2x(1-2)
2x-2x+1 = 2x(-1)
2x-2x+1 = – 2x
Please help! What is the area of this figure?
Answer and explanation please! <3
Answer:
19 units²
Step-by-step explanation:
Divide into three shapes:
Large rectangle BEFA
Large triangle - BCE
Small triangle - CDE -
BEFA = 4x3 = 12
BCE = 1/2x4x2 = 4
CDE = 1/2x3x2 = 3
12+4+3=19
PLEASE HELP ;(
If x varies directly as y, find
x when y = 8.
x = 11 when y = -3
X =
Answer:
1638 or 1368!
Step-by-step explanation:
How are land parcels valued?
1. Joshua has a ladder that is 12 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 11.8 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 75°. Will the ladder be safe at this height? Show your work and draw a diagram to support your answer.
Answer:
So we'll use trig to solve this because it's a right triangle. The hypotenuse is the ladder (h) and the two smaller sides are the ground and the vertical wall (w).
That angle ladder makes with the ground = €
SOH: sin € = opposite/hypotenuse
No the ladder won't be safe!!!
Now let's make it safe:
The ladder's length (w) is constant, so stays 12
So now let's ask in an inequality what height will be safe (75° or less)
what does that mean?? well as long as you put the ladder against the wall so that the height from ground to top of the ladder is < 11.6 ft!!
Hope that helps! :-D
Step-by-step explanation:
Answer:
not safe it is 78.5 degrees
Step-by-step explanation:
Find the missing side x=
Change the following expression to an equivalent expression in exponential form
Answer:
12^4/5
Step-by-step explanation:
When doing this you put the number the base is raised to on top of the fraction and the root number on the bottom
Find the slope of the line.
Answer:
1/3 is the slope
Step-by-step explanation:
hope this helps
Ashton bought 5 cans of olive oil. Each can had a radius of 3.2 inches and was 15 inches tall. Find the total cubic inches of olive oil Ashton had.
Step-by-step explanation:
A can is a cylinder.
Volume of a can = Volume of Cylinder
[tex] = \pi {r}^{2} h[/tex]
Given Radius = 3.2 inches and height = 15 inches,
Volume of one olive oil can =
[tex]\pi( {3.2}^{2} )(15) \\ = 153.6\pi {in}^{3} [/tex]
Volume of 5 olive oil cans = 5 x volume of one olive can
[tex] = 5 \times 153.6\pi \\ = 768\pi {in}^{3} [/tex]
I will just leave the answer in terms of pi as I'm not sure if you need to round off your answers.
A cell phone provider classifies its customers as Low users (less than 400 minutesper month) or High users (400 or more minutes per month). Studies have shownthat 80% of the people who were Low users one month will be Low users the nextmonth, and that 70% of the people who were High users one month will be Highusers the next month.
(a) Set up the 2x2 stochastic matrix with columns and rows labeled L and H that displays these transitions
(b) Suppose that, during the month of January, 50% of the customers were Low users. What percent of the customers will be Low users in February? In March? (Type an integer or decimal for each matrix element.)
1. The stochastic matrix for the given transitions is:
[tex]T = \left[\begin{array}{ccc}0.80 & 0.20\\0.30&0.70 \end{array}\right]\\[/tex]
2. 40.0% people in February and 32.0% people in March will be the low users if there are 50% low users in January.
It is given that,
80% of the people who were Low users one month will be Low users the next month.
That means for the transition low-low (L-L)
p = 0.80
So, for Low-high transition (L-H)
p = 1-0.80 = 0.20
It is also given that 70% of the people who were High users one month will be High users the next month.
That means, p = 0.70 for the transition high-high (H-H)
Then for H-L transition, p = 1-0.70 = 0.30
(a) The 2x2 stochastic matrix for these transitions is:
[tex]T = \left[\begin{array}{ccc}0.80 & 0.20\\0.30&0.70 \end{array}\right]\\[/tex]
(b) Given that 50% users are the low users in month of January.
[tex]\text{Percent of the customers will be Low users in February}= (\text{low users in month of January} \times \text{Probability of L-L transition.}) \times 100\%[/tex]= (0.50 x 0.80)x100%
= 0.4x 100%
=40.0%
Now, the percentage of people who will be low users in the month of march = (low users in February x probability of L-L transition)x100%
=(0.40x0.80)x100%
=0.32x100%
=32.0%
Hence, the percentage of people who will be low users in the month of February and in the month of March are 40.0% and 32.0% respectively.
Therefore, the results are:
1.2x2 stochastic matrix for the transitions is as:
[tex]T = \left[\begin{array}{ccc}0.80 & 0.20\\0.30&0.70 \end{array}\right]\\[/tex]
2. The percentage of people who will be low users in the month of February and in the month of March are 40.0% and 32.0% respectively.
Learn more about stochastic matrix here:
https://brainly.com/question/29737056
#SPJ4
Find the value of x
Answer:
x=80
Step-by-step explanation:
(x+30)=110 because they are vertically opposite angles.
x+30=110
x=110-30
x=80
Answer:
x = 80 degrees
Step-by-step explanation:
x + 30 = 110
- 30 = -30
x = 80 degrees
according to the Michigan DNR, the wolf population on Beaver Island can be modeled by the equation P= 1300(.87)^x. Is the population increasing or decreasing, and by what percent?
Answer:
The population is decreasing by 13%.
Step-by-step explanation:
The standard exponential equation can be modeled by:
y = A(1 ± r)^x
2. Jason can put his money in a savings account and earn about 12 cents in interest this month, or he can
loan it to Matt, who says he'll return the money plus $20 at the end of the month. He loans it to Matt.
a. The opportunity cost is
Answer:
12 cents
Step-by-step explanation:
opportunity cost of the next best option forgone when one alternative is chosen over other alternatives
by loaning matt the money he forgoes the opportunity to earn 12 cents in interest. this is his opportunity cost
in the diagram below given that XY = 30cm, XZY =30° and YZ = x, is it possible to solve for x using the theoram of pythagoras
Answer:
No, you need to know another angle to prove that it is a right triangle to use the Pythagorean theorem.
If you did have an additional side length, that needed angle could be calculated and then use the Pythagorean to prove.
Which equation has a slope of -1 and an x-intercept of (2,0)
Answer:
A (x+y=2)
Step-by-step explanation:
in order to see the slope value and to turn the equation into the slope-intercept form (y=mx+b). Basically we just solve for y and look at the coefficient of x. Then to see the value of the x-intercept we need to give y zero and then solve for x.
a) x+y=2
y=-x+2 (slope is -1)
when y=0 ; 0=-x+2 ; x=2 (x-int=2)
b) x-y=-2
y=x+2 (slope≠-1, it is +1 so this not the answer)
c) x+y=-2
y=-x-2 (slope is -1)
when y=0 ; 0=-x-2 ; x=-2 (x-int≠2 it is -2 so this not the answer)
d) x-y=2
y=x-2 (slope≠-1, it is +1 so this not the answer)
the answer is A (x+y=2)
Answer:
x + y = 2.
Step-by-step explanation:
Using the standard form
y = mx + b
the equation is
y = -1x + b
Now as the x intercept is (2, 0), x = 2 when y = 0 so:
0 = -1(2) + b
2 = b
b = 2
so we have
y = -x + 2
y + x = 2.