The area of a rectangle with side lengths 5/8ft. and 1/3 ft is: D. 5/24 ft².
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width or base of a rectangle.L represents the length or height of a rectangle.Substituting the given points into the area of rectangle formula, we have the following;
Area of rectangle = 5/8 × 1/3
Area of rectangle = 5/24 square feet.
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Find the 66th
term in the following
arithmetic sequence
-92, -85, -78, -71, ...
Answer:
The [tex]66[/tex]th term is [tex]363[/tex].
Step-by-step explanation:
To find the [tex]n[/tex]th term, the formula is [tex]7n - 99[/tex]. Since we want to find the [tex]66[/tex]th term, we can plug [tex]n[/tex] for [tex]66[/tex]. So our expression is now [tex]7 \cdot 66 - 99 =[/tex] [tex]66[/tex]th term. Solving this we have
[tex]462 - 99 = 66\text{th term}\\363 = 66\text{th term}\\[/tex]. Therefore, the [tex]66[/tex]th term is [tex]\boxed{363}[/tex].
Answer:
a₆₆ = 363
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 92 and d = a₂ - a₁ = - 85 - (- 92) = - 85 + 92 = 7 , then
a₆₆ = - 92 + (65 × 7)
= - 92 + 455
= 363
If f(x) = 2x² - x - 6 and g(x) = x² - 4, find f(x) = g(x).
OA.
B.
C.
2x+3
2
2x-3
#+2
2x+3
#+2
O D. 22-2
Jhayq
Answer:
Step-by-step explanation:
To find the value of x such that f(x) = g(x), we need to set the two functions equal to each other and solve for x.
First, let's define the variables:
f(x) = 2x² - x - 6 is a quadratic function with x as the variable.
g(x) = x² - 4 is also a quadratic function with x as the variable.
Now, to find the value of x such that f(x) = g(x), we set the two functions equal to each other:
2x² - x - 6 = x² - 4
Next, we simplify this equation by subtracting x² from both sides:
x² + x - 10 = 0
This is a quadratic equation, which we can solve for x using either the quadratic formula or by factoring.
Let's try factoring:
x² + x - 10 = (x + 5)(x - 2) = 0
So either x + 5 = 0 or x - 2 = 0. Solving for x, we find that:
x = -5 or x = 2
These are the two values of x such that f(x) = g(x).
Rectangle A: 2 * 3 Rectangle B: 8 * 12 Rectangle C: 5 * 7 Rectangle D: 10 * 12 Which pair of rectangles is similar?
Answer: your mom
Step-by-step explanation:
Scenario #1: Raul.
raul is a saver. he sets aside $100 per month during his career of 40 years to prepare for retirement. He does not like the idea of investing because he prefers to minimize his risk as much as possible so he puts his money in a savings account, which earns 1.5% interest per year.
1. what is the total balance in the account after 40 years?
2. how much of a total did Raul contribute himself?
3. how much money did Raul make through compound interest in this savings account?
4. identify one way Raul could have increased the total amount of money he made over 40 years. Explain your reasoning..
After 40 years, the account has a total balance of $49.450.80.
What is an interest?Any loans or borrowings come with interest. the portion of the loan's value that lenders use to calculate interest. By lending money (via a bond or certificate of deposit, for instance), or by depositing funds into an interest-bearing bank account, consumers can earn interest.
here, we have,
Let's assume that he starts with $0 in the account and makes a monthly contribution of $100 for 40 years, which is equal to 40 x 12 = 480 months.
The total contributions would be $100 x 480 = $48,000.
The interest earned on the account balance can be calculated as follows:
Interest = Account balance * Interest rate
At the end of each year, the interest is added to the account balance. So, after 40 years, the balance would be:
Year 1: $48,000 * 1.5% = $720
Balance = $48,000 + $720 = $48,720
Year 2: $48,720 * 1.5% = $730.80
Balance = $48,720 + $730.80 = $49,450.80
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This right circular cylinder has a radius of 8 in. And a height of 15 in. What is its volume, v?.
The volume of the cylinder is approximately 9,558.4 cubic inches.
The volume V of a right circular cylinder is given by the formula:
V = πr^2h
where r is the radius of the circular base and h is the height of the cylinder.
In this case, the radius is 8 inches and the height is 15 inches. Substituting these values into the formula, we get:
V = π(8^2)(15)
= π(64)(15)
= 3,040π cubic inches
Therefore, the volume of the cylinder is 3,040π cubic inches. If you want an approximate value, you can use the approximation π ≈ 3.14 and calculate:
V ≈ 3,040(3.14)
≈ 9,558.4 cubic inches
So, the volume of the cylinder is approximately 9,558.4 cubic inches.
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How many pounds are in 1
1⁄2 pounds and 8 ounces?
There are
pounds in 1 pounds and 8 ounces.
The solution is
n ID:
The number of pounds in [tex]1\frac{1}{2}[/tex] pounds and and 8 ounces is 2 pounds.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
We know that 1 pound = 16 ounces.
As there are [tex]1\frac{1}{2}[/tex] pounds=1.5×16= 24 ounces.
The total number of ounces in [tex]1\frac{1}{2}[/tex] pounds and 8 ounces is
24+8
32 ounces.
Now let us convert Ounces to pounds.
we divide the number of ounces by 16.
Therefore, 32 ounces is equal to 32/16 = 2 pounds.
Hence, 2 pounds will be there in [tex]1\frac{1}{2}[/tex] pounds and 8 ounces
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I will give brainliest and ratings if you get this correct
The quotient rule is proved below.
What is derivative of a function?In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
Given is the expression -
Q(x) = F(x)/G(x)
Quotient rule -Quotient rule in calculus is a method used to find the derivative of any function given in the form of a quotient obtained from the result of the division of two differentiable functions. Mathematically, for a function f(x), we can write -
f'(x) = [u(x)/v(x)]' = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]²
Proof -Now, let f(x) = u(x) and g(x) = v(x).
Q(x) = u(x)/v(x)
Q(x) = u(x) v⁻¹(x)
Using the product rule -
Q'(x) = u'(x) v⁻¹(x) + u(x) {d/dx v⁻¹(x)}
Q'(x) = u'(x) v⁻¹(x) + u(x) (-1)(v(x)⁻²) v'(x)
Q'(x) = u'(x)/v(x) - u(x)v'(x)/v²(x)
Q'(x) = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]²
Therefore, the quotient rule is proved above.
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product p of three numbers x ,y,and z
Answer:
p = x(y)(z)
Step-by-step explanation:
product is multiplication.
multiplication has no specific order.
Sue has 18 sweets.
Tony also has 18 sweets.
Sue gives Tony x sweets.
Sue then eats 5 of her sweets.
Tony then eats half of his sweets.
Write expressions for the number of sweets Sue and Tony now have.
Sue:
Tony:
Answer:
Step-by-step explanation:
18-5=13
18-9=9
Graph the function f(x) = -x² - 2. Complete the table of function values below. x f(x) -2 -1 0 1 2 Use the graphing tool to graph the function.
The graph of the quadratic function is on the image at the end.
How to graph the quadratic function?Here we want to graph the quadratic function:
f(x) = -x² - 2
To do so, we can complete the table of values by evaluating the function.
if x = ±2 then:
f(±2) = -(±2)² - 2 = -4 - 2 = -6
if x = ±1
f(±1) = -(±1)² - 2 = -1 - 2 = -3
if x = 0
f(0) = -(0)² - 2 = - 2 = -2
Then we have the points:
(-2, -6), (-1, -3), (0, -2), (1, -3), (2, -6)
Now just graph these points and connect them with a curve. The graph of the parabola is below.
1. Is Event 1 and Event 2 Mutually Exclusive of each other? Event 1: Pre- Schooler is a girl Event 2: Pre- Schooler prefers the color blue to the color pink Select one: a. No, A girl pre-schooler can prefer the color blue to the color pink. b. Yes, The gender of pre-schooler has no affect on color preference c. Yes, Girls prefer the color pink to the color blue 2. 70 preschoolers were asked whether they preferred blue or pink. 35 Girls chose pink as preferred color, 15 girls chose blue as preferred color, 5 boys chose pink as preferred color, and 15 boys chose blue as preferred color. Assuming one of the pre-schoolers is chosen at random determine the probability of choosing a preschooler that is a girl that prefers the color blue. Round answer to 2 decimal places.
The probability of choosing a preschooler who is a girl and prefers the color blue is 0.3 or 30%.
The total number of preschoolers who were asked about their color preference is 70. Out of these, 35 girls chose pink, 15 girls chose blue, 5 boys chose pink, and 15 boys chose blue.
To find the probability of choosing a girl who prefers blue, we need to use the formula:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Here, the favorable outcome is choosing a girl who prefers blue. We can see that 15 girls chose blue as their preferred color. Out of these, we need to choose a girl, so the total number of favorable outcomes is 15.
The total number of outcomes is the total number of preschoolers, which is 70. Out of these, the number of girls is 35+15=50. Therefore, the total number of outcomes where a girl can be chosen is 50.
Putting these values in the formula, we get:
Probability = 15/50 = 0.3
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Complete Question;
70 preschoolers were asked whether they preferred blue or pink.
35 Girls chose pink as preferred color, 15 girls chose blue as preferred color, 5 boys chose pink as preferred color, and 15 boys chose blue as preferred color.
Assuming one of the preschoolers is chosen at random determine the probability of choosing a preschooler that is a girl that prefers the color blue. Round answer to 2 decimal places.
Use the distributive property to evaluate 4(2x - 1) when x = 6.
O44
04
40
O 47
The value of the expression 4(2x - 1) when x = 6 is 44. Option A
What are algebraic expressions?Algebraic expressions are defined as expressions that are made up of coefficients, terms, variables, factors and constants.
They are also identified with arithmetic operations, such as;
AdditionMultiplicationDivisionSubtractionBracketParenthesesFrom the information given, we have that;
4(2x - 1)
expand the bracket, we get;
8x - 4
Substitute the value of x as , we have;
8(6) - 4
Multiply
48 -4
Subtract the values
44
Hence, the value is 44
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18 What is the solution to the system of equations x - y = -1 and x-3y = - 13?
A. (5, 6)
B.
(6,5)
C. (7,8)
D.
(8,7)
Suppose you have $200 with which you can buy shares of stock from two companies:
ABC Hot Chocolate Company and XYZ Lemonade. Each company's stock currently sells for $100 per share. If the temperature next year is lower than average, the stock price for ABC will increase by $20, and the stock price for XYZ will not change.
If the temperature next year is higher than average, the stock price for XYZ will increase by $20, and the stock price for ABC will not change. There is a 50% chance that it will be colder than average next year, and a 25% chance that it will be warmer than average.
If you purchase two shares of ABC stock and no shares of XYZ stock, there is a _____ chance that your gain will be $40. Otherwise, your gain will be _____.
1) 50%, $0
2) 25%, $20
3) 75%, $30
4) 50%, $20
The chances are that your gain will be $40 if you purchase two shares of ABC stock and no shares of XYZ stock, and if it is not $40 the gain is:
1) 50%, $0
2) 25%, $20
3) 75%, $30
4) 50%, $20
So, the option (4) 50%, $20 is the correct option.
The given question is asking what the chances are that your gain will be $40 if you purchase two shares of ABC stock and no shares of XYZ stock, and what the gain will be if it is not $40.
Mathematically, this can be broken down as follows:
There is a 50% chance that the temperature will be lower than average, in which case the stock price for ABC will increase by $20. Thus, the expected gain from investing in ABC is 50% x $20 = $10.
There is a 25% chance that the temperature will be higher than average, in which case the stock price for XYZ will increase by $20. Since you are not investing in XYZ, your expected gain from this is 0.
Therefore, the expected gain from investing in ABC and not investing in XYZ is 50% x $10 + 25% x $0 = $10 + $0 = $10.
Since you are investing in two shares of ABC stock, your expected gain is 2 x $10 = $20. Thus, there is a 50% chance that your gain will be $40, and otherwise your gain will be $20.
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One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 2.2 cubic feet of water weigh:
In pounds?
In tons?
So far I Havn't received the correct answer yet.
Find the equation of the line L
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture above
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{-3}-\underset{x_1}{(-1)}}} \implies \cfrac{1 +1}{-3 +1} \implies \cfrac{ 2 }{ -2 } \implies - 1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{- 1}(x-\stackrel{x_1}{(-1)}) \implies y +1 = - 1 ( x +1) \\\\\\ y+1=-x-1\implies {\Large \begin{array}{llll} y=-x-2 \end{array}}[/tex]
A bank developed a model for predicting the average checking and savings account balance as balance= −17,732 + 367×age + 1,300×years education + 0.116×household wealth
The interpret the numbers in this model is -17,732 is a constant amount credited from the savings account, 367 is the amount saved per year of age, 1300 is the amount saved per year of education.
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. In mathematics, a linear equation is an equation that may be put in the form [tex]{\displaystyle a_{1}x_{1}+\ldots +a_{n}x_{n}+b=0, } where x_{1}, \ldots, x_{n} are the variables, and {\displaystyle b, a_{1}, \ldots, a_{n}}[/tex] are the coefficients, which are often real numbers.
Given that;
The equation of savings account balance as balance= −17,732 + 367×age + 1,300×years education + 0.116×household wealth.
Now,
-17,732 is a constant amount credited from the savings acount
367 is the amount saved per year of age
1300 is the amount saved per year of education
0.116 is the amount save per household wealth
Therefore, the following are the interpretations of the equation.
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What is the approximate horizontal distance between Amelia and Brendon? Explain your reasoning
The approximate angle of elevation if Brendan looks up at the tower is 20.03°
What is an elevation?The angle of elevation in math is "the angle formed between the horizontal line and the line of sight when an observer looks upwards is known as an angle of elevation".
We know that, sinθ = opposite/hypotenuse
Here, sinx° = 50/146
sinx° =0.34246575342
x = sin⁻¹(0.34246575342)
x = 20.0271724581
x = 20.03°
Therefore, the approximate angle of elevation if Brendan looks up at the tower is 20.03°
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"Your question is incomplete, probably the complete question/missing part is:"
Amelia and Brendon are both on the ground looking at The top of a tower point D. Amelia is at point A and Brendan is at point B.
What is the approximate angle of elevation in Brendan looks up at the tower explain your reasoning.
Which represents the solution to the inequality 5.1(3+2.2x)>-14.25-6(1.7x+4)?
X=<-2.5
x>2.5
(-2.5,~)
(-~,2.5)
Step-by-step explanation:
Hope it helps :) #CarryOnLearning
1/4 (8x plus 2) = 20
Answer:
x = 9.75
Step-by-step explanation:
1 / 4 * ( 8x + 2) = 20
( 8x + 2) = 20 / (1/4)
8x + 2 = 20 * 4
8x + 2 = 80
8x = 78
x = 9.75
Answer:
x=39/4 (39 over 4 as a fraction)
A bag of garden soil weighs 42 pounds and holds 2 cubic feet. Find the weight of 15 bags in kilograms and the (((volume of 15 bags in cubic yards.)))
Answer:
he weight of 15 bags of garden soil in kilograms is 285.75 kilograms, and the volume of 15 bags in cubic yards is 1.111 cubic yards.
Step-by-step explanation:
To find the weight of 15 bags in kilograms, we can first convert the weight of one bag from pounds to kilograms and then multiply by the number of bags:
1 pound = 0.453592 kilograms
So the weight of one bag in kilograms is:
42 pounds * 0.453592 kilograms/pound = 19.05 kilograms
The weight of 15 bags in kilograms is:
15 bags * 19.05 kilograms/bag = 285.75 kilograms
To find the volume of 15 bags in cubic yards, we can first convert the volume of one bag from cubic feet to cubic yards and then multiply by the number of bags:
1 cubic yard = 27 cubic feet
So the volume of one bag in cubic yards is:
2 cubic feet / 27 cubic feet/cubic yard = 2 / 27 = 0.07407 cubic yards
The volume of 15 bags in cubic yards is:
15 bags * 0.07407 cubic yards/bag = 1.111 cubic yards
Therefore, the weight of 15 bags of garden soil in kilograms is 285.75 kilograms, and the volume of 15 bags in cubic yards is 1.111 cubic yards.
Which of the following complexe numbers is equal to (4 + 3i)(5 - 2i)?
20 + i
20+6i
26 + i^2
26 + 7i
Answer:
The product of (4 + 3i)(5 - 2i) can be calculated using the distributive property:
(4 + 3i)(5 - 2i) = 4 × 5 + 4 × -2i + 3i × 5 + 3i × -2i
= 20 - 8i + 15i - 6i^2
= 20 + 7i - 6(-1)
= 26 + 7i
So the answer is (4) 26 + 7i.
I believe the answer is (d) 26 + 7i.
There are marbles of four different colors in a bag. The
ratio of red to white to blue marbles is 3:4:5. There are half
as many green marbles as there are blue marbles. What is
the least possible number of marbles in the bag?
(A) 12
(B) 24
(C) 29
(D) 58
Answer:
(C) 29
Step-by-step explanation:
Please help:) calculus asking about delta functions
The required solution of the given expression δ = 0.0002. as of the given conditions
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given |x - 3| < δ, we want to find a value of delta such that |5x - 15| < 0.001.
Starting with the inequality |x - 3| < δ, we can substitute x = 3 + delta or x = 3 - δ. Let's consider the case x = 3 + δ,
|5x - 15| = |5(3 + δ) - 15|
= |15 + 5δ- 15|
= |5δ|
Now, we want |5δ| to be less than 0.001. So, we can divide both sides of the inequality by 5,
|5δ|/5 < 0.001/5
|δ| < 0.001/5
Therefore, if the delta is less than 0.001/5, we have |5x - 15| < 0.001.
Similarly, if x = 3 - delta, we have:
|5x - 15| = |5(3 - δ) - 15| = |15 - 5δ - 15| = |-5δ|
|-5δ|/5 < 0.001/5
|δ| < 0.001/5
So, if δis less than 0.001/5, then |5x - 15| < 0.001 for both x = 3 + delta and x = 3 - δ.
Therefore, if |x - 3| < 0.001/5, then |5x - 15| < 0.001.
So, δ= 0.001/5 = 0.0002.
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Complete the sentence below.
0.075 is a hundred times smaller than
Answer:
0.075 is a hundred times smaller than 7.5
Step-by-step explanation:
You made a big batch of slime for all of your friends. You have 7.2 cups of slime and 36 containers. What is the unit rate? (How much is in each container?) Enter your answer as a decimal in the box. The units are cups per container. Do not put the units.
Using the unitary method, we found that the unit rate of slime is 0.2 cups per container.
What is meant by the unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value. Recognizing the units and values is crucial when using the unitary technique to a problem.
Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. The unitary approach must be applied whenever we need to determine the ratio of one quantity to another.
Given,
Number of cups of slime = 7.2
Number of containers = 36
Unit rate = Amount of slime in each container
Using the unitary method we can find the unit rate.
7.2 cups = 36 containers
1 container = 7.2/36 = 0.2 cups.
Therefore using the unitary method, we found that the unit rate of slime is 0.2 cups per container.
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Using The Distance Formula: What is the length of AB
With A(3,4) and B(-4,6)
A'B' = D2/3 (AB)
What else would need to be congruent to show that AABC= APQR by SSS?
B
A
A. AC = PQ
B. AB BA
C. BC= QR
D. ZAZP
C
Q
P
R
Given:
AC PR
AB=PQ
The condition which satisfy the congruency of the given triangle is
BC≈QR.
What is congruency of triangles?Two triangles are said to be congruent if all the corresponding sides are equal and all the corresponding angles are equal. The symbol of congruency is '≅'
To show that triangle ABC≈triangle PQR by SSS,
In this type of congruency, all the sides of the triangle ABC is equivalent to the all the sides of the triangle PQR.
Given, AC≅PR, AB≅PQ.
The another one condition is BC≅QR.
Hence, the condition which satisfy the congruency of the given triangle is BC≈QR.
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Find the exact value of x
Answer:
When it comes to right trangles, to find the value of x, what ever 9 plus x is, it is equal to 24.
You want to subtract 9 and 24 to get the x value:
24 - 9 = 15
x = 15
Step-by-step explanation:
Hope it helps! =D
Hi there, here's your answer:
Given a right angled triangle
With the hypotenuse as 24 units and one of the legs as 9 units
To find:
The 3rd side denoted as 'x'
Solution:
We use Pythagoras Theorem:
[tex]a^2 + b^2 = c^2[/tex]
Where a and b are the legs and c is the hypotenuse.
We know the value of c and b
And a = x
Thus,
[tex]x^2 = c^2 - b^2[/tex]
[tex]x^2 = 576 - 81\\[/tex]
[tex]== > x^2 = 495\\[/tex]
Or
[tex]x = \sqrt{495} = 3\sqrt{55} = 22.248[/tex] units
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A bank is offering 2.5% simple interest on a savings account. If you deposit $5000, how much interest will you earn in 4 years?
• $50,000
• $500
• $125
• $12,500
[tex] \large \blue{ \large\tt{C ) \$500}}[/tex]
_____________
[tex] \: [/tex]
Given:-
[tex] \rm{Principal= \bold {5000}}[/tex][tex] \rm{Time= \bold 4}[/tex][tex] \rm{Intrest Rate= \bold { 2.5}}[/tex][tex] \: [/tex]
By using formula:-
[tex] \boxed{ \rm{ \pink{Simple \: interest= \frac{Principal × Time × Rate}{100}}}}[/tex]
[tex] \: [/tex]
Solution:-
[tex] \rm{SI = \frac{PTR}{100} }[/tex][tex] \: [/tex]
[tex] \rm{SI= \frac{50 \cancel{00}×4×2.5}{1 \cancel{00}} }[/tex][tex] \: [/tex]
[tex] \rm{SI=50×4×2.5}[/tex][tex] \: [/tex]
[tex] \underline{\boxed{ \rm{ \red{SI= 500}}}}[/tex][tex] \: [/tex]
hope it helps!:)
Answer: the answer is c.$500 hope that helps !
Step-by-step explanation: I took the test
