Answer:
$50
Step-by-step explanation:
We will call x the original price of the sunglasses.
We can create the equation below using the information given.
[tex]x*\frac{30}{100} =15[/tex]
Now solve for x.
[tex]x = 15*\frac{100}{30}[/tex]
[tex]x = \frac{100}{2}[/tex]
[tex]x=50[/tex]
Classify the following functions as growth or decay: f(x) = 10 (6/7)^x, g(x)= 1/3e^x, h(x)=5e^-x, k(x)= -10(6/7)^x
It is known that any exponential function with the form f(x)=a^x is an increasing function while a function of the form g(x)=a^(-x) is a decreasing function.
Furthermore, it a function h(x) is increasing, then the function -h(x) is decreasing. By analogy, if a function k(x) is decreasing, then -k(x) is increasing.
Now let's analyze the functions from the problem.
[tex]\text{ Let }f(x)=10\cdot(\frac{6}{7})^x[/tex]Since (6/7)^x is increasing and the multiplying factor of 10 is positive, then the function f(x) is also increasing.
Use these rules to find whether each function is increasing or decreasing.
Remember that increasing functions are used to represent growth while decreasing functions are used to represent decay.
What is a different common Denominator you could use in problem 2
Answer:
what is the problem ???
Step-by-step explanation:
Please help me I was sick today and missed out on class and I don’t understand this question
Answer: 72 i think
Step-by-step explanation:
How many months does it take $428 to double at a simple interest rate of 12%
When $428 doubles, it means that the
Fill in the blanks below with the correct units.(a) The school bus had a mass of about 9000 ?(b) Last week, Ravi drove about 13?to visit his uncle.(c) Goran added 5 ?e of cream to his coffee.
The first unit is kilograms because the bus is really heavy.
The second is kilometers because meters are too small.
The third one is milliliters because liters are too much for ice cream.
HELP ME QUICK!! I’LL MARK YOU BRAINLIEST!!
3-8. Find the distance between each pair of points if they were graphed on a number line. Represent your work
using absolute value symbols.
a. -10 and 10
b. -15 and -7
1. Write the regression2.r =3. what does the r mean?I predict there will be a [blank] relationship between [blank] and [blank] I think it’s because [blank] and I’m gonna send a photo about my graphing points
First of all, we have to find the mean of x values.
According to the given graph, the x values are: 0, 1, 2, 2, 3, 3, 4, 5, 6, 7.
So, the mean is
[tex]\bar{x}=\frac{0+1+2+2+3+3+4+5+6+7}{10}=\frac{33}{10}=3.3[/tex]The mean of x values is 3.3.
The y values are: 2, 2, 3, 4, 4, 4, 5, 6, 8, 9.
The mean would be
[tex]\bar{y}=\frac{2+2+3+4+4+4+5+6+8+9}{10}=\frac{44}{10}=4.4[/tex]The mean of y values is 4.4.
Now, we find the standard deviation for x values and y values.
[tex]undefined[/tex]The equation for the line that has a slope of -3/8 and passes through (0, 10) is: y = -3/8x + 10 : y = 3/8 x - 10
The standard form of expression equation of a straight line is;
[tex]y\text{ = mx+c}[/tex]where;
m is the slope
c is the intercept
Given
slope m = -3/8
Next is for us to get the y- intercept of the line. This is done by subtituting the slope and the point (0,10) given into the equation y = mx+c and calculating c as shown;
[tex]\begin{gathered} y\text{ = mx+c} \\ 10\text{ = -3/8(0)+c} \\ 10\text{ = 0+c} \\ c\text{ = 10} \end{gathered}[/tex]Next is to get the equation of the line by substituting m = -3.8 and c= 10 into the standard form of the equation as shown;
[tex]\begin{gathered} y\text{ = mx+c} \\ y\text{ = -}\frac{3}{8}x+10 \end{gathered}[/tex]Hence the first option is correct
If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is
given by y = 88t - 16t².
When does the ball reach its maximum height? (Round to two decimal places)
If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is given by y = 88t - 16t².The ball will reach its maximum height at 121 feet.
Maximum heightGiven equation:
y = 88t - 16t²
Maximum height dy/dt = 0
88-32t = 0
32t = 88
t = 88/32sec
t = 2.75sec
Hence,
Maximum height attained by the ball :
Maximum height attained by the ball = 88(2.75)-16(2.75)²
Maximum height attained by the ball = 242 - 121
Maximum height attained by the ball = 121 feet
Therefore the maximum height is 121 feet.
Learn more about maximum height here: https://brainly.com/question/12446886
#SPJ1
find all real and complex zeros for f(x)=x^3-x^2+3x-3
The real and complex zeros for the function given as .f(x) = x³ - x² + 3x - 3 are x = 1 and x = ±i√3, respectively
How to determine the zeros of the function?The equation of the function is given as
f(x) = x³ - x² + 3x - 3
Group the terms of the function in two's
So, we have the equation
f(x) = (x³ - x²) + (3x - 3)
Factor each group in the function
f(x) = x²(x - 1) + 3(x - 1)
Factor out x - 1
f(x) = (x² + 3)(x - 1)
Set to 0
(x² + 3)(x - 1) = 0
This gives
x² = - 3 and x = 1
Evaluate the roots
x = ±i√3 and x = 1
Hence, the zeros of the equation are x = ±i√3 and x = 1
Read more about zeros of function at
https://brainly.com/question/16550963
#SPJ1
Can you check work please?
When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). So all we do is make both x and y negative.
[tex]\begin{gathered} K(-4,-3)\rightarrow K^{\prime}(4,3) \\ L(-3,-1)\rightarrow L^{\prime}(3,1) \\ M(0,-3)\rightarrow M^{\prime}(0,3) \end{gathered}[/tex]
12. The perimeter of a triangle with sides 5x-1, 5x-1, 2.2x +10, and the perimeter of a square with a side length of 6.5x -11.8 are the same. What is the value of x?
The value of x is 4.
The perimeter of any shape is the sum of lengths of all its sides.
We are provided with the sides of triangle i.e., 5x-1, 5x-1 and 2.2x +10.
So, The perimeter of a triangle = sum of length of all three sides = (5x-1) + (5x-1) + (2.2x +10)
The perimeter of a triangle = 12.2x + 8 equation 1
Also, we are provided with the side of square i.e., 6.5x -11.8.
The perimeter of a square = 4 (side) = 4 (6.5x - 11.8)
The perimeter of a square = 26x - 47.2 equation 2
As per question,
Perimeter of a triangle = Perimeter of a square
12.2x + 8 = 26x - 47.2
13.8x = 55.2
x = 4
So we can write, the value of x is 4.
To know more about Perimeter of a square refer to the link:
https://brainly.com/question/479529
#SPJ1
find the answer to this problem (15/16) - ( -3/16)
A. 3/4
B. -3/4
C. -1 1/8
D. 1 1/8
the original price of an article was 240.00. The price is increased by 12½%. The new price of the article is?
Answer:
The new price of the article is $270
Step-by-step explanation:
270-240/240
x 100% = 12.5%
12.5x240/100
= 30
Sarah enrolled $10,000 worth of debt with National Debt Relief. We negotiated with the creditors and reduced the debt by 50%. Sarah’s fee for our services was 25% of the enrolled debt ($10,000). How much did Sarah end up saving after reducing her debt and paying us our fee?*
Answer:
7500$
Step-by-step explanation:
a group of people are waiting in line for a movie premier. every 14th person in line will win a free movie ticket . every 10th person will receive a gift card of 30 dollars. which person is the first to win both prizes.if there are 200 people in line how many will receive both prizes?
In order to determine which person is the first to win both prizes, you have to find the least common multiple to both numbers 14 and 10.
To determine what is the least common multiple number you proceed as follow:
You list different multiples of each number 14 and 10.
For 14: 14 28 42 56 70 84 98 112
For 10: 10 20 30 40 50 60 70 80
The least common multiple is 70, becasue is the first common number in each list.
Hence the 70th person in the line will win both prizes.
A certain standardized test has a mean of 421 and a standard deviation of 18. For a student to score higher than 30.85% of those who took the exam, what score would be necessary?
The score required for the exam so that the score is higher than 30.85% is 412 for certain standardized test.
What is defined as the z-score?A Z-Score is a measurable statistic of a score's connection to the mean among a set of scores.A Z-score can tell a trader whether a value is characteristic for a given data set or atypical.In overall, a Z-score of less than 1.8 indicates that a company may be on the verge of bankruptcy, whereas a score nearer to 3 indicates that a company is in good financial standing.The formula for finding the z-score is;
z = (x - μ)/σ
x = sample size
μ = mean of the population
σ = standard deviation of the population.
The given values are-
μ = 421
σ = 18
Probability = 30.85% = 0.3085
Check the z-score from the negative z table for 0.3085
z score = -0.5
Put the values in z formula and find x.
z = (x - μ)/σ
-0.5 = (x - 421)/18
Simplifying;
x = -9 + 421
x = 412
Thus, the score required for the standardized test is found as 412.
To know more about the z-score, here
https://brainly.com/question/24213960
#SPJ10
A teacher is organizing binders for her students. She has 54 pieces of lined paper, 36 pieces of grid paper, and 72 dividers. What is the greatest number of identical binders that she can make? Please help!
Using the highest common factor, the greatest number of identical binders that the teacher can make is 18.
What is the highest common factor?The highest common factor or multiple of the given numbers is the highest number that can divide them without a remainder.
We know that 2, 9, and 18 can divide 54, 36, and 72 without leaving a remainder.
We can see that the highest common factor is 18.
When we divide 54 by 18, the quotient is 3. If you divide 36 by 18, the quotient is 2. When you divide 72 by 18, the result is 4.
The number of lined paper = 54 pieces
The number of grid paper = 36 pieces
The number of dividers = 72 dividers
The common factors of 54, 36, and 72 are 2, 9, and 18.
The highest common factor of 54, 36, and 72 is 18.
Thus, 18 binders containing 3 pieces of lined paper, 2 pieces of grid paper, and 4 dividers can be made from the collection, using their HCF.
Learn more about the highest common factor at https://brainly.com/question/219464
#SPJ1
[tex]3-\sqrt{x} 5[/tex]
The value of the expression given as 3 - √x⁵ is 3 - x^2√x
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression?The expression is given as
3 - √x⁵
Express 5 as the sum of 4 and 1
So, we have the following equation
3 - √x⁵ = 3 - √x^(4 + 1)
Apply the law of indices to expand the equation
So, we have the following equation
3 - √x⁵ = 3 - √(x^4 * x)
Next, we expand the equation
So, we have the following equation
3 - √x⁵ = 3 - √x^4 * √x
Evaluate the square root of x^4
So, we have the following equation
3 - √x⁵ = 3 - x^2 * √x
Evaluate the product
So, we have the following equation
3 - √x⁵ = 3 - x^2√x
Hence, the value of the expression is 3 - x^2√x
Read more about expressions at
https://brainly.com/question/4541471
#SPJ1
The graph of a linear function is given below.What is the zero of the function ?A. -3B. -3/2C. -2/3D. -2
Using the graph, we can deduce the following:
• x-intercept: x = -2
,• y-intercept: y = -3
Let's determine the zero of the function.
The zero of a function can be said to be the root of the function. It is also called the x-intercept of the function.
The zero of a function is the point the line crosses the x-axis.
From the graph the x-intercept is at x = -2.
Therefore, the zero of the function is:
x = -2
ANSWER:
D. -2
7. On February 12th, a fire occurred at a local dry cleaning plant and the inpatient service days for the localhospital (120 beds) was reported to be 130. What is the bed occupancy rate for February 12th? Round toone decimal place.
We can use the following formula:
[tex]_{\text{ }}Bed_{\text{ }}occupancy_{\text{ }}rate=\frac{\#_{\text{ }}of_{\text{ }}inpatient_{\text{ }}days_{\text{ }}for_{\text{ }}a_{\text{ }}given_{\text{ }}period}{_{\text{ }}avalaible_{\text{ }}beds\times\#_{\text{ }}days_{\text{ }}in_{\text{ }}the_{\text{ }}period}_{}\times100[/tex]So:
[tex]_{\text{ }}Bed_{\text{ }}occupancy_{\text{ }}rate=\frac{130}{120\cdot365}\times100[/tex]Answer:
0.3%
Horatio left a campsite, hiking at a rate of 1 mile per hour. Ivan left 3 hours later, hiking at a rate of 2 miles per hour. How long will it take Ivan to catch up to Horatio?
Ivan will catch up to Horatio in 3 hours .
In the question ,
it is given that
speed of Horatio is 1 miles per hour
speed of Ivan is 2 miles per hour .
and Ivan leaves 3 hours late than Horatio .
Let "t" be the time ( in hours ) taken for Ivan to meet Horatio ,
So, the distance covered by Ivan will be 2*t .
Since Horatio left 3 hours before so the time taken for Horatio to meet Ivan is (t+3).
So, the distance covered by Horatio will be 1*(t+3) .
The distance covered for Horatio and Ivan will be equal ,
which means
2*t = 1*(t+3)
2t = t + 3
2t - t = 3
t = 3
Therefore , Ivan will catch up to Horatio in 3 hours .
Learn more about Equation here
https://brainly.com/question/8484205
#SPJ1
Find the value of (-3/8) x (+8/15)
A. -1/5
B. -1/3
C. 11/15
D. 11/23
Answer: [tex]\Large\boxed{A. -\dfrac{1}{ 5}}[/tex]
Step-by-step explanation:
Given expression
[tex]-\dfrac{3}{8} \times \dfrac{8}{15}[/tex]
Combine the fractions
[tex]=\dfrac{-3\times 8}{8 \times 15}[/tex]
Cancel out the 8 on both the numerator and denominator
[tex]=\dfrac{-3}{ 15}[/tex]
Divide 3 on both the numerator and denominator
[tex]=\dfrac{-3\div 3}{ 15\div 3}[/tex]
[tex]=\Large\boxed{-\dfrac{1}{ 5}}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Through how many radians does the minute hand of a clock rotate from12:40 PM to 1:10 PM?o10- 10The minute hand rotates through radians.(Simplify your answer. Type an exact answer in terms of Use integers orfractions for any numbers in the expression)-10
As you can see in the given figure the minute hand of a clock rotate from 12:40 to 1:10 formig a straigth angle.
A straight angle in radians is π radians.
Then, the minute hand rotates π radiansa student has 200 Naira if someone gives her 160 Naira how much will she have if someone gives her x Naira how much would she have
Answer:
360 naira hope it will be helpful
Step-by-step explanation:
Find the equation for the circle with a diameter whose endpoints are (5,5) and (3,−5).
The equation of the circle in standard form whose center is at (h, k) = (4, 0) is (x - 4)² + y² = 26.
How to derive the standard equation of the circle based on the coordinates of diameter endpoints
In this question we find the coordinates of the endpoints of the diameter of the circle, then, the center of the circle is the midpoint of the line segment. The center of the circle is found by midpoint formula:
(h, k) = 0.5 · (5, 5) + 0.5 · (3, - 5)
(h, k) = (4, 0)
And the radius of the circle is determined by Pythagorean theorem:
r = √[(4 - 5)² + (0 - 5)²]
r = √[(- 1)² + (- 5)²]
r = √26
Then, the equation of the circle in standard form is describe below:
(x - h)² + (y - k)² = r²
If we know that (h, k) = (4, 0) and r = √26, then the equation of the circle is:
(x - 4)² + y² = 26
To learn more on equations of the circle: https://brainly.com/question/23799314
#SPJ1
2320 is what percent of 2000
Provide the correct reason for the statement in line 1. (please help)
Answer:
d) given
Step-by-step explanation:
nothing has been done yet, the statement is given as stated above the statement
Solve the equation for x.
6(x + 3) - 8 = 4x + 2(4 + x)
Hello! So...
We are given the following to solve:
Solve for x.
[tex]6(x+3)-8=4x+2(4+x)[/tex]
_______________________________________________________
1. Expand both sides of the equation.
[tex]6(x+3)-8=6x+10[/tex]
[tex]4x+2(4+x)=6x+8[/tex]
[tex]6x+10=6x+8[/tex]
______________________________
2. Subtract 10 from both sides.
[tex]6x+10-10=6x+8-10[/tex]
_______________________________
3. Simplify.
[tex]6x=6x - 2[/tex]
_______________________________
4. Subtract 6x from both sides.
[tex]6x-6x=6x-2-6x[/tex]
_______________________________
5. Simplify.
[tex]0=-2[/tex]
^Notice, the sides are not equal in the solution. This being said, there would be no solution.
___________________________________________________
Hope this helps! If you need anything else, feel free to comment below. Thanks and good luck!
help meeeeeeeeeeeeeeeeeeeeeee
Answer:
600
Step-by-step explanation:
[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]