An exponential function is a function in which the variable is in the exponent. The general form of an exponential function is f(x) = ab^x, where a and b are constants.
The variable x is the exponent, meaning that it is raised to a certain power, resulting in the variable being in the exponent. In this function, the value of the function increases or decreases at a rate that is proportionate to the current value of the function.
This type of function is commonly used in modeling growth or decay in various fields such as biology, economics, and physics. The exponential function generates a sequence that is exponential in nature, the rate of change of the function is directly proportional to the value of the function.
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A number $x$ is equal to $7\cdot24\cdot48$. What is the smallest positive integer $y$ such that the product $xy$ is a perfect cube?
Take the prime factorization of [tex]x[/tex].
[tex]x = 7\times24\times48 = 7\times(2^3\times3)\times(3\times2^4) = 2^7\times3^2\times7[/tex]
If [tex]xy[/tex] is a perfect cube, then the smallest [tex]y[/tex] that makes this happen is [tex]y=2^2\times3\times7^2 = \boxed{588}[/tex]. We "complete" the cube by introducing just enough factors to get each prime power to be a multiple of 3.
Answer: 588
Step-by-step explanation:
Which expression can be used to find 52% of 230?
Hello,
52% of 230 = 52/100 × 230 = 0,52 × 230 = 119,6
Answer:
230 : 100 * 52 =
Step-by-step explanation:
Which expression can be used to find 52% of 230?
The expression is: 230 : 100 * 52 =
Do the points (1,2) , (51,27) and (91,48) lie on a straight line? give reason for your answer
Answer:
No. They cannon be on the same straight line.
Step-by-step explanation:
As explained in the attached graphic, the slopes are slightly different between the three points.
Find the surface area of a rectangular prism with a height of 16 feet, a width of 10 feet, and a length of 13 feet.
The surface area of a rectangular prism with a height of 16 feet, a width of 10 feet, and a length of 13 feet is 996 ft².
A = Surface area
l = Length
w = Width
h = Height
A = 2 ( w l + h l + h w )
= 2 · ( 10 · 13 + 16 · 13 + 16 · 10 )
= 996 ft²
The gap occupied by using a dimensional flat surface is referred to as the region. it's far measured in rectangular gadgets. The location occupied by using a 3-dimensional object by means of its outer floor is referred to as the surface location.
The surface vicinity of a strong object is a degree of the total vicinity that the surface of the item occupies.
The floor location is the overall location included via all of the faces of a 3-d item. As an example, if we need to discover the amount of paint required to paint a cube, then the surface on which the paint will be implemented is its floor place. it is continually measured in square gadgets.
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Let theta be an angle in quadrant iv such as sin theta = -5/8. find the exact value of sec theta and cot theta
Using a trigonometric identity, it is found that the secant and the cotangent of the angles are given as follows:
[tex]\sec{\theta} = \frac{8\sqrt{39}}{39}[/tex][tex]\cot{\theta} = -\frac{\sqrt{39}}{5}[/tex]Which trigonometric identity relates the sine and the cosine of an angle?The following identity is used, considering an angle [tex]\theta[/tex].
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
In this problem we are given the sine, then the cosine can be found as follows:
[tex]\left(-frac{5}{8}\right)^2 + \cos^2{\theta} = 1[/tex]
[tex]\cos^2{\theta} = 1 - \frac{25}{64}[/tex]
[tex]\cos^2{\theta} = \frac{39}{64}[/tex]
[tex]\cos{\theta} = \pm \sqrt{\frac{39}{64}}[/tex]
In the fourth quadrant, the cosine is positive, hence:
[tex]\cos{\theta} = \frac{\sqrt{39}}{8}[/tex].
What is the secant of an angle?The secant of an angle [tex]\theta[/tex] is one divided by the cosine of the angle, hence:
[tex]\sec{\theta} = \frac{1}{\cos{\theta}} = \frac{1}{\frac{\sqrt{39}}{8}} = \frac{8}{\sqrt{39}} \times \frac{\sqrt{39}}{\sqrt{39}} = \frac{8\sqrt{39}}{39}[/tex]
What is the cotangent of an angle?The cotangent of an angle [tex]\theta[/tex] is the cosine divided by the sine of the angle, hence:
[tex]\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}} = \frac{\frac{\sqrt{39}}{8}}{-\frac{5}{8}} = -\frac{\sqrt{39}}{5}[/tex]
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The prism shown in the diagram has a volume of 39 units^3. What is the volume of the pyramid? Explain your reasoning. I WILL GIVE BRAINLIEST ASAP FOR A QUICK ANSWER
The volume of the pyramid is 13 units³.
What is the volume of the pyramid?
A pyramid is a 3-dimensional shape that is made up of a rectangular base and 4 triangular faces. The volume of a pyramid is one-third that of a prism.
Volume of a pyramid = 1/3 x prism
1/3 x 39 = 13
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7. Find the equation of the line passing through the
points P(-2,7) Q(2,-3)
Answer: y=[tex]-\frac{5}{2} x+2[/tex]
Step-by-step explanation:
Use the equation of the line format: y = mx + b
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
[tex]m=\frac{-3-(7)}{2-(-2)}[/tex]
[tex]m=\frac{-10}{4}[/tex]
simplified
[tex]m=\frac{-5}{2}[/tex]
in order to find B:
[tex]y = -(\frac{5}{2}) *(-2)+b[/tex]
Insert value of y:
[tex]7 = (-\frac{5}{2} ) * (-2) +b[/tex]
Rewrite:
[tex]-\frac{5}{2} * -2 - b=7[/tex]
Cancel the common factor of 2:
[tex]-5 * -1 +b = 7[/tex]
Multiply -5 by -1:
[tex]5 + b= 7[/tex]
Subtract 5 from both sides:
[tex]b = 7-5\\b=2[/tex]
Now substitute values of m, and the final answer is:
[tex]y = -\frac{5}{2}x + 2[/tex]
Daphne is calculating the total asset turnover ratio of a company. Under which accounting principle would she value the assets of the company at their original cost? A. accrual method of accounting B. historical cost accounting C. business entity concept D. going concern concept
The accounting principle she would use to value the assets of the company at their original cost is historical cost accounting.
What is historical cost accounting?Historical cost accounting is an accounting method for recording the value of fixed assets under US GAAP where the value of an asset on a balance sheet is equal to the cost of acquiring the asset.
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A cylinder has a height of 17 feet and a radius of 6 feet. What is its volume? Use ≈ 3.14
and round your answer to the nearest hundredth.
Answer:
1921.68 [tex]ft^{3}[/tex]
Step-by-step explanation:
V = pi*r*r*h
= 3.14*6*6*17
= 1921.68
Need help with number 3 inequalities with variables on both sides
Answer:
x ≤ 2
Step-by-step explanation:
We are given the inequality:
[tex]\displaystyle{2x-3 \leq \dfrac{x}{2}}[/tex]
First, get rid of the denominator by multiplying both sides by 2:
[tex]\displaystyle{2x\cdot 2-3\cdot 2 \leq \dfrac{x}{2}\cdot 2}\\\\\displaystyle{4x-6 \leq x}[/tex]
Add both sides by 6 then subtract both sides by x:
[tex]\displaystyle{4x-6+6 \leq x+6}\\\\\displaystyle{4x \leq x+6}\\\\\displaystyle{4x-x \leq x+6-x}\\\\\displaystyle{4x-x \leq 6}\\\\\displaystyle{3x \leq 6}[/tex]
Then divide both sides by 3:
[tex]\displaystyle{\dfrac{3x}{3} \leq \dfrac{6}{3}}\\\\\displaystyle{x \leq 2}[/tex]
Therefore, the answer is x ≤ 2
Answer: [tex]x \leq 2[/tex]
Step-by-step explanation: Given [tex]2x - 3 \leq \frac{x}{2}[/tex], we multiply 2 by both sides to cancel out the 2 in the denominator (multiplying by a number in a fraction turns it into 1, and since the denominator is one, it is the same as saying the number [or variable] on the numerator by itself.)
We then get [tex]4x - 6 \leq x[/tex].
Adding 6 to both sides, we get [tex]4x \leq x + 6[/tex].
Subtracting x from both sides, we get [tex]3x \leq 6[/tex]
Dividing by 3 from both sides, we get [tex]x \leq 2[/tex]
Hope this helped!
Alex scored 40 marks out of 60 in a spelling test pet scored 65% in the same test who did better
Based on the test by result, Alex did better in the test by scoring 66.67%
PercentageAlex = 40 out of 60Percentage scored by Alex = 40/60 × 100
= 0.66666666666666 × 100
= 66.6666666666666
= 66.67%
my Percentage scored by pet = 65%Therefore, Alex did better in the test
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Find the nth term of the arithmetic sequence (an) whose initial term a and common difference d are given below. What is the forty-fifth term?
a₁ = 2; d = 1/4
Answer:
a₄₅ = 13
Step-by-step explanation:
The n-th term of an arithmetic sequence with first term a₁ and common difference d is given by the formula ...
aₙ = a₁ +d(n -1)
SetupYou want the 45th term where a₁ = 2 and d = 1/4. Putting these values into the formula gives ...
a₄₅ = a₁ +d(n -1) = 2 +(1/4)(45 -1)
SolutionEvaluating this expression, we have ...
a₄₅ = 2 +44/4 = 2 +11
a₄₅ = 13
The 45th term of the sequence is 13.
The forty-fifth term of the sequence whose initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex] is [tex]13[/tex]
How to find the nth term of the Arithmetic series?
The nth term of the arithmetic series is find by [tex]Tn = a+(n-1)d[/tex] where Tn is the nth term of the series a is called the initial number and is the common difference between two number. n is the number of term of that arithmetic series.
In the given series initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex]
We have the find the forty-fifth term of the given series.
= [tex]Tn=a+(n-1)d[/tex]
= [tex]Tn = 2+(45-1)\frac{1}{4}[/tex]
= [tex]Tn=2+44\cdot\frac{1}{4}[/tex]
= [tex]Tn = 2+11[/tex]
= [tex]Tn = 13[/tex]
So, the forty-fifth term of the sequence whose initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex] is [tex]13[/tex]
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Which algebraic expression has a term with a coefficient of 9?
• A. 6 + X- 9
• B. 6x - 9
C. 6(x + 5)
• D. 9x ÷ 6
Answer:
D
Step-by-step explanation:
Coefficient is the number next to the variable, and D is the only one where that number is 9. All the others are 6.
Point W is located at (-5, -3).
Select all of the following that are 5 units from point W.
Choose all answers that apply:
A. (-5, 2)
B. (−8,−5)
C. (-5, 0)
The point that is 5 units from W is (A) (-5, 2)
How to determine the points?The point is given as:
W= (-5, -3)
A point 5 unit from W can be any of the following
W' = (-5 ± 5, -3)
W' = (-5, -3 ± 5)
When the above expressions are evaluated, we have:
W' = (0, -3), (-10, -3), (-5, 2) and (-5, -8)
Hence, the point that is 5 units from W is (A) (-5, 2)
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The graph of f(x) = 1/3
is reflected vertically, compressed horizontally by a factor of 5, shifted
right 2 units and down 6 units. Write the equation of the new graph.
The transformed function is defined by:
g(x) = -f(x/5 - 2) - 6
Where f(x) is the given function.
How to get the equation of the transformed function?Here we start with the function:
f(x) = (1/3)*x
(I don't know if this is the actual function, but that does not matter, I will solve it in a general way).
If first, we reflect it vertically, then the new function is:
g(x) = -f(x).
If now we compress it horizontally by a factor of 5, then we get:
g(x) = - f(x/5)
Now we shift it 2 units to the right, then:
g(x) = -f(x/5 - 2)
Finally, we shift it down 6 units, then we get:
g(x) = -f(x/5 - 2) - 6
That is the general form of the function g(x).
Replacing f(x) by what is defined above, we get:
g(x) = -(1/3)*(x/5 - 2) - 6
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The Hartman family is saving $400 monthly for Ronald’s college education. The family anticipates they will need to contribute $20,000 toward his first year of college, which is in 4 years. Which best explains whether the family will have enough money in 4 years?
The family will not have enough money. They will have saved only $16,000.
The family will not have enough money. They will have saved only $19,200.
The family will likely have enough money. They will have saved $16,000 and have accumulated interest.
The family will likely have enough money. They will have saved $19,200 and have accumulated interest.
The statement which best explains whether the family will have enough money in 4 years is; The family will not have enough money. They will have saved only $19,200.
SavingsAmount Hartman family saves monthly = $400Amount needed = $20,000Number of years = 4Number of months = 4 × 12 = 48Amount saved in 4 years = Amount Hartman family saves monthly × Number of months
= $400 × 48
= $19,200
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The statement which best explains whether the family will have enough money in 4 years is; The family will not have enough money. They will have saved only $19,200.
SavingsAmount Hartman family saves monthly = $400Amount needed = $20,000Number of years = 4Number of months = 4 × 12 = 48Amount saved in 4 years = Amount Hartman family saves monthly × Number of months
= $400 × 48
= $19,200
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Riley bought a 7 1/2 pounds of clay for the students in her pottery class. She then divided the clay into 4 equal pieces for her students to use for making vases and pots. How much did each piece weigh?
Answer:
1.857 pounds
Step-by-step explanation:
If the clay is divided into 4 equal parts, we divide 7.5lbs by 4: 7.5/4 = 1.857 lbs
The table above represents what type of function?
A.
linear and nonlinear
B.
linear
C.
neither linear nor nonlinear
D.
nonlinear
B because it’s a linear graph.
Two boys, John and Peter, are running a 100-meter race. In the first race that they run John beats Peter by 5 meters. To make things fair, the next time they race John stands 5 meters behind the starting line. If they run at the same speed as the first race, who will win the second race
Second time john wins the race because he runs in the race with constant speed as same speed they run in 1st race.
According to the statement
We have given that the John and Peter, are running a 100-meter race.
In the first race that they run John beats Peter by 5 meters. and the next time they race John stands 5 meters behind the starting line.
Here the both participant's speed remain same in both races.
So, We have to find that the If they run at the constant speed as the first race, who will win the second race
So, for this purpose
According to the statement
in first race john beats the peter and wins the race and if they start the second race with the same speed then it is clear that the second time john won the race.
So, Second time john wins the race because he runs in the race with constant speed as same speed they run in 1st race.
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Find the midpoint between
-7 + 4i
and
3 - 2i
Answer:
-2+i
Step-by-step explanation:
-7+4i represents (-7,4) and 3-2i represents (3,-2).
So, the midpoint is (-2,1), which represents -2+i.
Johnny created a chart using stick people to depict the frequency of the data. What type of chart did Johnny create
Johnny created a Tally marks chart.
A frequency distribution table displays the frequency of each data set in an organized way. It helps us to find patterns in the data and also enables us to analyze the data using measures of central tendency and variance. The first step that a mathematician does with the collected data is to organize it in the form of a frequency distribution table. All the calculations and statistical tests and analyses come later.
Tally Marks are used to keep a track of numbers in the quickest possible way. Tally marks are used for counting and are represented as a set of five lines in which there are four vertical lines (one vertical line is made for each of the first four numbers) and the fifth number is represented by a diagonal line across the previous four numbers. It can be understood through the given figure
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6.6x 10⁵ in standard notation
Answer:
660000
Step-by-step explanation:
Based on an 8-hour day, the number of hours worked in a hospital food service department was 55,267/yr., and the total number of hours paid was 59,995/yr. The actual number of productive FTEs was:
That year FTE was 26.
According to statement
Labor hours worked that year = 55,267
Total number of hours paid that year = 59,995
The total number of hours during the year
8 hours × 5 days × 52 weeks = 2080 hours
Now we find the FTE per year
So, FTE/YEAR = Labour works on that year / total number of hours in year
Substitute the values in it then
FTE/YEAR = 55267/2080
FTE/YEAR = 26
So, That year FTE was 26.
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The math team wraps gifts as a way to raise money for traveling to competitions. They offer two choices: a plain wrapping or a decorative wrapping with bows. The table represents the money raised over a busy shopping weekend.
A 3-column table titled Gift-Wrapping Fundraiser has 3 rows. The first column is labeled Plain Gifts Wrapped with entries 10, 25, 16. The second column is labeled Decorative Gifts Wrapped with entries 9, 12, 12. The third column is labeled Total Raised in dollars with entries 47, 86, 68.
Which statement describes the amounts the team charged for wrapping gifts?
Answer:
Step-by-step explanation:
We will assume that the first two columns are the numbers sold for Plain Wrapping and Decorative Wrapping. The third colum does not equal the sum of the first two, so we'll assume it is the total paid for both options. Let set the price of Plain Wrapping to x and the Decorative Wrapping to y. The number of gift wrappings times the cost per warpping is the product of x or y timers the number wrapped as shown in columns 1 and 2.
Take the first row and set it as an equation:
10x+9y = 47 [10 Plain Wraps and 9 Decorative Wraps bring a total of $47]
Do the same for the second and third rows:
25x + 12y = 86, and
16x +12y = 68
===========
We can take any equation and rearrange it to isolate one of the 2 variables, x or y. I'll pick 10x = 47-9y and isolate x:
10x = 47-9y
x = (47-9y)/10
-------------------
Now use this definition of x in another equation. I'll use 25x + 12y = 86.
25x + 12y = 86
25(47-9y)/10 + 12y = 86 [since x = (47-9y)/10 from above]
117.5 - 22.5y + 12y = 86
-10.5y = -31.5
y = 3 [the price for decorative wrapping is $3]
If y = 3, then we can use this in any of the equations to find x:
x = (47-9y)/10
x = (47-9(3))/10 [Use y = 3]
x = (47-27)/10
x = 2 [The price for plain wrapping is $3]
======================
Check to see if these values will expalin the total value of the three rows of numbers:
CHECK:
______UNITS____ $2 each $3 each
PlainW DecG Total PlainW ($) DecG ($) Total ($)
x y x y
10 9 $47 $20 $27 $ 47 OK
25 12 $86 $50 $36 $ 86 OK
16 12 $68 $32 $36 $ 68 OK
The values work. Merry Christmas.
Answer:
The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.
Step-by-step explanation:
just did it in edg
Using the quadratic formula, solve the
equation below to find the two possible
values of t.
6x^2-35=-11x
Give each value as a fraction in its
simplest form.
Answer:
x= 19/12, -41/12
Step-by-step explanation:
I'm guessing x is "t".
The quadratic formula is x=(-b+-sqrtb^2-4ac)/2a I know that this is hard to read sorry!
Plug in a, b, and c.
Oh yeah, first convert it to the form Ax^2+bx+c
so 6x^2-35=-11x
6x^2+11x-35=0
(-11+-sqrt11^2-(-4*6*35))/2*6
Simply: (-11+-sqrt 121+840)/12
(-11+-sqrt961)/12
(-11+-31)/12
-11+30=19
-11-30=-41
x= 19/12, -41/12
Which statement can you use to conclude that quadrilateral xyzw is a parallelogram
Answer: Option (4)
Step-by-step explanation:
A quadrilateral with two pairs of opposite congruent sides must be a parallelogram.
Jenny made $120 for 8 hours of work. How much would jenny make for 40 hours of work? Use a proportion to show your work in the space provided.
Answer:
$600
Step-by-step explanation:
For 8 hours she makes $120
For 1 hour she makes $120÷8 = $15
For 40 hours she makes $15 × 40 = $600
Our final answer is $600
Hope this helped and have a good day
please help me to get an answer thanks
Answer:
A=P(1+in)
A=13000(1+6/100×9)
A=press calculator
Consider the expansion of (x^2+px-3)(3x-5),where p is a constant.If the coefficient of x of the expansion is -44,find the value of p
Answer:
p = 7
Step-by-step explanation:
(x² + px - 3)(3x - 5)
each term in the second factor is multiplied by each term in the first factor, that is
x²(3x - 5) + px(3x - 5) - 3(3x - 5) ← distribute parenthesis
= 3x³ - 5x² + 3px² - 5px - 9x + 15 ← collect like terms
= 3x³ +x²(3p - 5) - x(5p + 9) + 15
given the coefficient of the x- term is - 44 , then
-(5p + 9) = - 44 ← - (5p + 9) is th coefficient of x in the expansion
- 5p - 9 = - 44 ( add 9 to both sides )
- 5p = - 35 ( divide both sides by - 5 )
p = 7
You’re taking a 33 question multiple choice test. Each question has 4 choices. Clueless on 1 question, you decide to guess. What’s the chance you’ll get it right?