Answer:
Step-by-step explanation:
To find the base of the exponential function F(x) = b^x, we need to use the information that its graph contains the point (1/3, 2). We can use this information to solve for b.
Since the graph passes through the point (1/3, 2), we can set x = 1/3 and y = 2 in the equation F(x) = b^x:
b^(1/3) = 2
Taking the cube root of both sides, we get:
b = (2)^3 = 8
So the base of the exponential function F(x) = b^x is b = 8, which means the correct answer is C) 8.
What needs to be done to an equation to find the slope and y intercept??
NEED HELP ASAP
Answer:
C. Solve for the variable y.
Step-by-step explanation:
You want to know what needs to be done to an equation to find the slope and y-intercept.
Slope-intercept formThe slope-intercept form of the equation for a line is ...
y = mx + b
This is a polynomial equation written in standard form with the terms in decreasing order of the power of the variable. In this equation, the coefficient 'm' is the slope of the line, and the constant 'b' is the y-intercept on the graph.
This equation can be obtained from other forms of the equation for a line by solving for y and arranging the terms to match this form. That is, to find the slope and y-intercept, what needs to be done is ...
C. Solve for the variable y.
__
Additional comment
The description "standard form" as used above applies to polynomials in general. Specific polynomial equations, as for lines, circles, ellipses, hyperbolas, have their own "standard form."
The form called "standard form" for a linear equation is ...
ax +by = c
where a, b, c are mutually prime integers with a > 0. In the case of a horizontal line, b > 0.
<95141404393>
A hole in a steel plate has a diameter of 1.166 cm
at 23.00 ∘C
At what temperature is the diameter of the hole equal to 1.164 cm
?
will give brainliest
So here we have a hole in a steel plate with a diameter of 1.166 cm. So we need to find the temperature at what temperature is the diameter of full equal to 1.165 cm. So you're given is D. I. That is equal to initial diameter. That is equal to 1.166 cm. and temporary Germany shirt temperature is equal to 23°C and DF is equal to 1.165 m. This is the final diameter. So you only need to find the value of P. F. So we know that whole diameter very nice linearly with And nature. So here we can say DFS equal to D. I multiplied by one plus alpha. They're dirty. Yeah, I'll find that coefficient of thermal expansion. So here we can say it this is for steel And the value of alpha is equal to 13, multiplied by 10, raised to -6. So D F. Is equal to B. I multiplied plus the I'm multiplied by alpha, multiplied by delta T. So here we can see it D F minus D. I. That is the initial final diameter minus initial diameter divided by D. I. Alpha. That is equal to delta P. So this will be where to tell 30. That is equal to -6.59717. multiplied by 10° to -5 divided by And there's do -6. So here the key Is equal to -65.9717 degree. So here P f minus T I is equal to minus 65.9717 degree. The T.F will be equal to 23 -65.9717. So therefore final temperature that this T.F is equal to -42.8717 degrees Celsius. So therefore this is the answer to the question. So here we can say hands, final temperature Is equal to -42.8717°C.
13. Landon is 6 ft. tall and measures his shadow to
be 8.3 ft. long. At the same time of day, he
measures a tree's shadow to be 17.6 ft. long. How
tall is the tree?
Answer: 12.72 ft.
Step-by-step explanation:
[tex]\frac{6}{8.3} = \frac{x}{17.6} \\\\ 8.3x= 105.6\\\\x= 12.72[/tex]
Financial planning case 2-2
Victor Hernandez Considers a Career Change
Victor is somewhat satisfied with his sales career and has always wondered about a career as a teacher in a public school. He would have to take a year off work to go back to college to obtain his teaching certificate, and that would mean giving up his $40,000 salary for a year. Victor expects that he could earn about the same income as a teacher. Round your answers to the nearest dollar.
What would his annual income be after 12 years as a teacher if he received an average 4 percent raise every year? Round Future Value of a Single Amount in intermediate calculations to four decimal places. (Hint: Use Appendix A-1.)
$
Victor also could earn $3,000 each year teaching during the summers. What is the accumulated future value of earning those annual amounts over 12 years assuming a 5 percent raise every year? Round Future Value of a Series of Equal Amounts in intermediate calculations to four decimal places. (Hint: Use Appendix A-3.)
$
Answer: Victor's annual income after 12 years as a teacher would be $47,564 if he received an average 4 percent raise every year.
The accumulated future value of earning $3,000 each year teaching during the summers over 12 years with a 5 percent raise every year would be $41,592.
Step-by-step explanation:
To calculate Victor's annual income after 12 years as a teacher, we need to find the future value of his starting salary of $40,000 after 12 years with an average 4 percent raise every year.
Using the formula for the future value of a single amount (FV = PV * (1 + r)^n), where PV is the present value, r is the interest rate, and n is the number of years, we can calculate the future value as follows:
FV = $40,000 * (1 + 0.04)^12 = $47,564
So, Victor's annual income after 12 years as a teacher would be $47,564 if he received an average 4 percent raise every year.
To calculate the accumulated future value of earning $3,000 each year teaching during the summers over 12 years with a 5 percent raise every year, we need to use the formula for the future value of a series of equal amounts (FV = A * (1 + r)^n - 1 / r), where A is the annual payment and r is the interest rate.
Plugging in the values, we get:
FV = $3,000 * (1 + 0.05)^12 - 1 / 0.05 = $41,592
So, the accumulated future value of earning $3,000 each year teaching during the summers over 12 years with a 5 percent raise every year would be $41,592.
In ADEF, J is the intersection of the three medians. If EI = 33, find JI.
D
Q
H
F
The value of JI in the given triangle is 11.
What is a triangle?A triangle is a polygon with three sides, vertices and angles.
Given that, in a triangle DEF, J is the intersection of the three medians.
EI = 33, we are asked to find the value of JI,
Since, all the median is intersecting at J, therefore, J is the centroid.
We know that, the centroid divides each median into two parts, which are always in the ratio 2:1.
Therefore,
Let, EI = 3x,
JI = x,
Therefore, JI = 11
Hence, the value of JI in the given triangle is 11.
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The complete question is :
In Δ DEF, J is the intersection of the three medians. If EI = 33, find JI.
Figure is attached
If the California Current moves at 0.25 cm/s, how fast is that in knots?
Answer:
0.4850 knots.
Step-by-step explanation:
To convert the speed of the California Current from centimeters per second to knots, we can use the conversion factor of 1 knot = 0.514444444 cm/s.
So, 0.25 cm/s * 1 knot / 0.514444444 cm/s = 0.4850 knots.
Therefore, the California Current moves at a speed of approximately 0.4850 knots.
Write the set using set-builder notation
(9, 18, 27, 36, ...}
How do i do this
The set builder notation is A = { 9x | x ∈ N } which is a set of all x’s containing multiples of 9
What is union and intersection of sets?The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets
The intersection of two sets is a new set that contains all of the elements that are in both sets
Given data ,
Let the set be represented as A
Now , the value of A is
A = { 9 , 18 , 27 , 36 , ... }
The set A contains all the positive multiples of 9
So , let x be the set of natural numbers and the value of A is
A = { 9x | x ∈ N } , and
A = set of all x’s containing multiples of 9
Hence , the set builder notation is { 9x | x ∈ N }
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find the sum of the series. make sure you use the formula and show your work for credit.
please help me I didn't get this at all!
Answer:
The sum of the series is 260.
------------------------
Each term of given series is expressed as:
tₙ = 3n - 1This is an arithmetic progression with 13 terms and the first and last terms are:
t₁ = 3*1 - 1 = 2t₁₃ = 3*13 - 1 = 38Use the sum of the first terms of AP formula:
Sₙ = (t₁ + tₙ)*n/2S₁₃ = (2 + 38)*13/2 = 40*13/2 = 20*13 = 260Answer:
The sum of the series is 260.
Step-by-step explanation:
[tex]\displaystyle \sum^{13}_{n=1}(3n-1)[/tex]
The given sigma notation means:
Sum of the series with nth term (3n - 1), starting with n = 1 and ending with n = 13.As (3n - 1) is linear, the series is arithmetic.
The first term (n = 1) is:
a₁ = 3(1) - 1 = 2The second term (n = 2) is:
a₂ = 3(2) - 1 = 5The third term (n = 3) is:
a₃ = 3(3) - 1 = 8… and the last term (n = 13) is:
a₁₃ = 3(13) - 1 = 38Therefore, we need to find 2 + 5 + 8 + ... + 38.
Since we know that the first term, a, is 2, the last term, l, is 38, and the common difference, d, is 3, we can use the sum of the first n terms formula to calculate the sum of the series of the first 13 terms.
[tex]\begin{aligned}\text{Using:} \quad S_{n}&=\dfrac{1}{2}n(a+l)\\\\\implies S_{13}&=\dfrac{1}{2}(13)(2+38)\\\\&=\dfrac{1}{2}(13)(40)\\\\ &=\dfrac{520}{2}\\\\&=260\end{aligned}[/tex]
Therefore, the sum of the series is 260.
In the figure below angle A and angle B make a right angle.
Suppose A = 2x - 8
and L B = 3x + 5.
Given this information the measure of B would be
degrees
The measure of ∠B of the right angle is 152°
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ABC
Now , the measure of ∠A = 2x - 8
The measure of ∠B = 3x + 5
And , angle A and angle B make a right angle
On simplifying the equation , we get
2x - 8 = 90
Adding 8 on both sides of the equation , we get
2x = 98
Divide by 2 on both sides of the equation , we get
x = 49
Substitute the value of x in equation , we get
∠B = 3 ( 49 ) + 5
The measure of ∠B = 152°
Hence , the angle is ∠B = 152°
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One number is 7 more than another number. The sum of these two numbers is 101. What are the numbers?
Answer:
54 and 47
Step-by-step explanation:
Lets first number be "x" and second number be "y"
x = y + 7
x + y = 101
(y + 7) + y = 101
2y + 7 = 101
2y = 94
y = 47
x = 47 + 7
x = 54
Selma wants to take her money out of the bank account with simple interest rate of 5% annually and put it in another account with compound interest rate of 8% compounded quarterly if the bank says closing the current account has a penalty of 5% at least how many years she let the money stay at the new account in order to recover the penalty paid using extra interest of the second?
Selma needs to leave the money in the new account for at least one year, option A. 1 to recover the penalty paid.
How did we get this assertion?Assuming Selma wants to recover the penalty paid using the extra interest earned in the new account, she needs to calculate the amount of time it will take for the new account's interest to make up for the penalty paid.
Let P be the initial amount of money in Selma's current account. The penalty for closing the account is 5% of P, which is 0.05P.
If Selma leaves the money in the current account for one year, she will earn simple interest of 5% of P, which is 0.05P. So at the end of the year, the balance in the current account will be P + 0.05P = 1.05P.
If Selma transfers the money to the new account, it will earn compound interest of 8% per year, compounded quarterly. The quarterly interest rate is 8%/4 = 2%.
After one quarter, the balance in the new account will be:
P*(1 + 2%/4) = P*1.02
After two quarters, the balance will be:
P1.02(1 + 2%/4) = P*1.02^2
After three quarters, the balance will be:
P1.02^2(1 + 2%/4) = P*1.02^3
After four quarters (i.e., one year), the balance will be:
P1.02^3(1 + 2%/4) = P*1.02^4
So at the end of one year, Selma will have 1.05P in the current account and P*1.02^4 in the new account.
To recover the penalty of 0.05P, Selma needs the balance in the new account to be at least 1.05P. That is,
P*1.02^4 >= 1.05P
Simplifying, we get:
1.02^4 >= 1.05
Taking the fourth root of both sides, we get:
1.02 >= 1.05^(1/4)
Using a calculator, we get:
1.02 >= 1.01298
So Selma needs to leave the money in the new account for at least one year to recover the penalty paid.
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Trigonometry question
The value of sin(tetha/2) is ±√½(1-8/√113)
What are half angles?In trigonometry, the half-angle formula is used to determine the exact values of the trigonometric ratios of angles such as 15° (half of the standard angle 30°), 22.5° (half of the standard angle 45°), and so on. If θ is an angle, then the half angle is represented by θ/2.
if tan(tetha) = 7/8
this means that 7 is the opposite and 8 is the adjacent
hyp² = opp² +adj²
hyp² = 49+64
hyp = √113
sin(tetha/2) = ±√1-cos(tetha))/2
= ±√1-(8/√113))/2
therefore the value is sin(tetha)/2
= ±√1-(8/√113))/2 or ±√½(1-8/√113)
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Is 8 a solution to 3/4x=6?
PLEASE GIVE BRAINLIEST!
thank you and have a good day :)
Answer:
YES, x = 8
Step-by-step explanation:
plug in 8 for x and see if both sides are equal
3/4 times 8 = 24/4 or 6
Answer:
Yes, 8 a solution to 3/4 x=6 !Step-by-step explanation:
If we solve it as....
[tex]\mathrm{\cfrac{3}{4}x=6}[/tex]
[tex]\mathrm{4\times\cfrac{3}{4}x=6\times\:4}[/tex]
[tex]\mathrm{3x=24}[/tex]
[tex]\mathrm{\cfrac{3x}{3}=\cfrac{24}{3}}[/tex]
[tex]\mathrm{x=8}[/tex]
Yes, 8 would be the solution!
___________________
Hope this helps!
If the radius of one of the semicircles is 7 meters, what is the circumference of one of the semicircle? asap 70 Ponits!!!!!!!!!!
10.99 m
21.98 m
87.92 m
43.96 m
Answer:
The circumference of one of the semicircles with a radius of 7 meters would be approximately 21.98 meters.
Step-by-step explanation:
The circumference of a circle can be calculated using the formula:
C = 2πr
where C is the circumference, π (pi) is approximately equal to 3.14, and r is the radius of the circle.
For a semicircle with a radius of 7 meters, the circumference can be calculated as follows: Because the semicircle is a half circle, then:
C = (2πr)/2= 3.14 × 7 = 21.98 meters
So, the circumference of one of the semicircles with a radius of 7 meters would be approximately 21.98 meters.
Answer:
The circumference of one of the semicircles is 21.98 m.
Step-by-step explanation:
The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle.
A semicircle is half a circle, therefore the length of the curved part of the circumference of a semicircle is half the circumference of a circle: πr.
Given the radius of one of the semicircles is 7 m and π ≈ 3.14, the circumference of the semicircle is:
⇒ C = 3.14 · 7
⇒ C = 21.98 m
A magician has a magic trick that uses an 18" length of string that is cut into two pieces. One piece is two inches longer that the other. Find the length of each piece. Use algebraic equations.
The length of each piece is 10 in and 8 in.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The total length of the string = 18 in
One piece = x + 2
Another piece = x
Now,
Solve for x.
x + 2 + x = 18
2x + 2 = 18
2x = 18 - 2
2x = 16
x = 8
Now,
One piece = 8 + 2 = 10 in
Another piece = 8 in
Thus,
The length of each piece is 10 in and 8 in.
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Graph the following conditions. Click on the graphic to choose the correct answer. [(x, y): x + y = 5) 4 -3 -2 -1 YA 6 5 4 3 2 + T -2 -3 A 5 19 - K 2 3 4 5 6 X
A graph of the equation under this condition {(x, y): x + y = 5)} is shown in the image attached below.
What is an ordered pair?In Mathematics, an ordered pair simply refers to a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.
Next, we would determine the ordered pairs that satisfies the given linear function in standard form.
When the value of x = 1, the output value of this linear function is given by;
y = 5 - x
y = 5 - 1
y = 4 ⇒ (1, 4)
When the value of x = 0, the output value of this linear function is given by;
y = 5 - x
y = 5 - 0
y = 5 ⇒ (0, 5).
When the value of x = 2, the output value of this linear function is given by;
y = 5 - x
y = 5 - 2
y = 0 ⇒ (2, 3).
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Identify the percent of change as an increase or a decrease.
9 points to 4 points
o increase
decrease
Find the percent of change. Round to the nearest tenth of a percent if necessary.
The percent of change is
%.
The percent of change from 9 points to 4 points is approximate -55.6%, indicating a decrease of 55.6%.
What is the Percent of change?
The percent of change is a measure that compares the difference between two values to the original, or initial, value. It is usually expressed as a percentage and indicates how much a value has increased or decreased from its initial value.
To find the percent of change from 9 points to 4 points, we need to first calculate the amount of change, which is the difference between the final value (4 points) and the initial value (9 points):
Amount of change = Final value - Initial value = 4 - 9 = -5
The negative sign indicates a decrease in value.
Next, we can calculate the percent of change using the formula:
Percent change = (Amount of change / Initial value) x 100%
Substituting the values we get:
Percent change = (-5 / 9) x 100% ≈ -55.6%
Hence, the percent of change from 9 points to 4 points is approximate -55.6%, indicating a decrease of 55.6%.
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A certain antihistamine is often prescribed for allergies. A typical dose for a 100-pound person is 22 mg every six hours. Following this dosage, how many 12.3 mg chewable tablets would be taken in a week?
Answer:
x = 50 tablets
Step-by-step explanation:
Ket's call the number of tablets taken in a week "x".
A typical dose for a 100-pound person is 22 mg every six hours, so in 24 hours, they would take 22 mg * 24 hours / 6 hours = 88 mg.
In one week, they would take 88 mg * 7 days = 616 mg.
And since each tablet is 12.3 mg, they would take 616 mg / 12.3 mg/tablet = 50 tablets in a week.
So the answer is x = 50 tablets.
Solve 7.59 divided by 7 with no remainders
Anota una magnitud vectorial y explica tu respuesta
A physical quantity with both magnitude and direction is called a vector quantity.
A vector quantity is a physical quantity that has both magnitude and direction. One example of a vector quantity is velocity, which is defined as the rate of change of an object's position with respect to time. Velocity is a vector quantity because it has both a magnitude (speed) and a direction (the object's motion). For instance, if an object is moving with a speed of 20 meters per second to the north, its velocity would be 20 meters per second north. If the object's direction changes to east, its velocity would become 20 meters per second east. Therefore, velocity is a vector quantity because its value depends not only on the speed of the object but also on the direction in which it is moving.
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Complete Question
Write down a vector quantity and explain your response.
What is the value of x in l-16l = x
Answer: |-16| =x
- (-16)= x
x = 16
Step-by-step explanation:
thank you
A woman has a total of $7,000 to invest. She invests part of the money in an account that pays 10% per year and the rest in an account that pays 11 per year. If the interest earned in the first year is $730 , how much did she invest in each account
The amount invested in the account that earns 10% interest is $4,000 and the amount invested in the account that earns 11% interest is $3,000.
How much is invested in each account?The system of equations that represent the information in the question is:
a + b = 7000 equation 1
0.1a + 0.11b = 730 equation 2
Where:
a = amount invested in the account that earns 10% interest
b = amount invested in the account that earns 11% interest
The elimination method would be used to solve the equations.
Multiply equation 1 by 0.1
0.1a + 0.1b = 700 equation 3
Subtract equation 3 from equation 2
0.01b = 30
Divide both sides of the equation by 0.01
b = 30 / 0.01
b = 3000
Substitute for b in equation 1:
a + 3000 = 7000
a = 7,000 - 3000
a = 4000
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Help!!
Write an equation to show the total cost, y, for x months.
YOU WIL GET BRAINLIEST!!
The equation to represent the total cost, y, for x months is y = 12x + 30.
From the given table, we can observe that the total cost increases by $12 for each additional month of usage.
This means that the rate of change, or the slope of the equation, is $12 per month.
We can represent this relationship using the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope (rate of change) is $12, and the y-intercept can be determined by examining the table. When x = 0 months, the total cost is $30. Therefore, the y-intercept is $30.
Putting it all together, the equation to represent the total cost, y, for x months is:
y = 12x + 30
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The sum of the digits in a two-digit number is 14. If you reverse
and double the original number, and then add the result to the
original number, the sum is 222. Find the original number. Please help me.
Answer:
The original number is 86.
Step-by-step explanation:
The only two-digit numbers whose digits sum to 14 are:
5968778695If we reverse and double the original number:
59 reversed is 95 → 95 × 2 = 19068 reversed is 86 → 86 × 2 = 17277 reversed is 77 → 77 × 2 = 15486 reversed is 68 → 68 × 2 = 13695 reversed is 59 → 59 × 2 = 118If we add the result of reversing and doubling the original number to the original number:
59 + 190 = 24968 + 172 = 24077 + 154 = 23186 + 136 = 22295 + 118 = 213As the sum of adding the result of reversing and doubling the original number to the original number is 222, the original number must be 86.
Find
(M.
f(x)=√√√x²-1
g(x)=√√√x-1
a. √√x+1
b. √√x-1
C.
d.
-X+1
1
X+1
The function operation (f/g)(x) in the functions f(x) = √( x² - 1 ) and g(x) = √( x - 1 ) is √( x + 1).
What is the function operation (f/g)(x) in the function?A function is simply a relationship that maps one input to one output.
Given the functions in the question;
f(x) = √( x² - 1 )g(x) = √( x - 1 )(f/g)(x) = ?To evaluate (f/g), replace the function designators in f/g with the actual functions.
(f/g)(x) = f(x) / g(x)
(f/g)(x) = ( √( x² - 1 ) ) / ( √( x - 1 ) )
Now, rewrite 1 as 1²
(f/g)(x) = ( √( x² - 1² ) ) / ( √( x - 1 ) )
Factor using difference of square
(f/g)(x) = ( √( (x - 1)(x + 1 ) ) / ( √( x - 1 ) )
Combine into a single radical
(f/g)(x) = √( ( (x - 1)(x + 1) ) / ( x - 1 ) )
Now, cancel out the common factors (x-1)
(f/g)(x) = √( (x + 1) / 1 )
(f/g)(x) = √( x + 1)
Therefore, the function operation (f/g)(x) is √( x + 1).
Option A) √( x + 1) is the correct answer.
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-10 -8 -6 -4 -2 0 2 4 6 8 10
Plot the integer -7 on the number line.
The distance between 0 and -7 is
The absolute value of -7 is
The magnitude of -7 is
Step-by-step explanation:
To plot the integer -7 on the number line, we can place it to the left of 0. The number line would look like this:
-10 -8 -7 -6 -4 -2 0 2 4 6 8 10
The distance between 0 and -7 is 7 units, since 0 is 7 units to the right of -7.
The absolute value of -7 is 7, since the absolute value of a number is its distance from 0 on the number line.
The magnitude of -7 is also 7, which is the same as its absolute value. The magnitude of a number refers to its size or absolute value, regardless of its sign. In this case, the magnitude of -7 is 7.
i just really need a help guys thank u mwa
Answer:
See below
Step-by-step explanation:
My man, how did you even get these numbers??? no whole number multiplied by 6.65 even equals 22??? Regardless, here's what I did.
a) r = 40/2 = 20
A = πr^2 = (3.14)(20)^2 = 1256
b) 1256/50 = 25.12 basically, 26
c) 26 x 6.65 = 172.9
Thoughts and prayers my guy. Keep trying
Answer:
A. 1256[tex]ft^{2}[/tex] B. 26 pounds C. $172.90
Step-by-step explanation:
PART A
1st find the radius of the area
radius = diameter / 2
r = 40/2
radius = 20ft
Area of circle = radius^2* pi
Area = 400 * 3.14
Area = 1256 [tex]ft.^{2}[/tex]
PART B
1256 / 50 = 25.12
Because we can only buy full pounds and we need the whole area to be reseeded, we round 25.12 to 26.
26 pounds of seeds will be needed to reseed the whole area.
PART C
Multiply the number of pounds of seeds needed to be bought by 6.65
26 x 6.65
$172.90 for the total cost of grass seeds
The store you are buying the item down offers you an installment plan.
The terms of the contract for the plan are:
• $50 down
• 12 payments
• Finance charge of $100
Interest = Finance Charge = ________________
Total Payment = Cost of item + Finance charge = _____________
Monthly Payment = (Total Payment – Down payment / 12 = __________
1) Based on the percentage of the downpayment, the total payment made for the store item is $1,100, which includes a finance charge or interest of $100.
2) The monthly payment for 12 installments is $87.50.
How the total payment is computed:The total cost of the item is based on the downpayment's equivalent percentage (proportion).
A proportion is the equation of two or more ratios.
Finance Charge (Interest) = $100
Downpayment = $50 or 5%
Installment period = 12 months
Cost of item = $1,000 ($50/5%)
Total payment = $1,100 ($1,000 + $100)
Monthly payment = $87.50 ($1,100 - $50)/12
Learn more about proportions and percentages at https://brainly.com/question/1496357.
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Question Completion:The downpayment is 5% of the total cost of the item.
Evaluate the limit limx approches 0 x square+ x over x
Step-by-step explanation:
If we use direct substitution, we will get
[tex] \frac{0}{0} [/tex]
Which is intermediate from so we must use.algebraic manipulation
Let's divide everything by x
We would get
[tex] \frac{x + 1}{1} [/tex]
So the limit as x approaches 0 is
[tex]1[/tex]
Proof using a graph:
As x gets close and closer to 0, f(x) approaches 1. Limits does not care about discontinuity, only what the function gets closer to.
13) A theater has 38 rows of seats. The first row has 25 seats, the second
row has 29 seats, the third row has 33 seats, and so on.
What is the total number of seats in the theater?
O3,762
O3,838
O 7,524
O 7,676
Answer:
Step-by-step explanation:
To find the total number of seats in the theater, we can use the formula for the sum of an arithmetic series, which is given by:
S = n/2 * (a_1 + a_n)
where n is the number of terms in the series, a_1 is the first term, and a_n is the last term.
In this case, the first term is 25 seats and the last term is 25 + (38-1) * 4 seats (since the number of seats in each row increases by 4 each time). So, we have:
n = 38 (the number of rows)
a_1 = 25
a_n = 25 + (38-1) * 4 = 25 + 37 * 4 = 25 + 148 = 173
Now, we can substitute these values into the formula:
S = n/2 * (a_1 + a_n) = 38/2 * (25 + 173) = 19 * 198 = 3,762
So, the total number of seats in the theater is 3,762, which corresponds to option O3,762.
