The equation of the line is (y - 1/12) = -4/3(x - 7/5).
What is the slope of a line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are represented by y and x, respectively.
Consequently, the formula for the change in the y-coordinate with respect to the change in the x-coordinate is
m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line can be depicted by
tan θ = Δy/Δx
So, the slope of a line is tan.
The given equation of a line is:
3x-4y=7
-4y = -3x + 7
y = 3/4 x - 7/4
The slope of the line is 3/4.
The slope of the line perpendicular to the given line is - 1/m = - 4/3
The point-slope of a line is y - y₁ = m(x - x₁).
The given point is (7/5,1/12)
The equation of the line is
(y - 1/12) = -4/3(x - 7/5)
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What is the location of point G, which partitions the directed line segment from F to D into an 8:5 ratio?
A number line goes from negative 5 to 10. Point D is at negative 4 and point F is at 9. A line is drawn from point D to point F.
The position of G in the given line segment is at point 1, which is between points F and D and the line segment between F and D in the ratio 8:5.
What is meant by line segment?
Two unique points on a line define the boundaries of a line segment. A line segment is a section of the path a line takes to join two locations. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.
Given, the locations of D and F on the line segment.
D = -4
F = 9
Number of units between F and D = 9 - (-4) = 13
Point G partitions the line segment from F to D in the ratio 8:5.
So distance of G from F = [8/(8+5)] * 13 = 8
Distance of G from D = [5/(8+5)] * 13 = 5
So from F, it is 8 units behind F = 9 - 8 = 1
from D, it is 5 units in front of D = -4 + 5 = 1
Therefore the position of G in the given line segment is at point 1.
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a toy manufacturer needs a piece of plastic in the shape of a right triangle with one leg 5 cm longer than the other and the hypotenuse 10 cm longer than the shorter leg. what is the perimeter of the triangle
The triangle's perimeter is roughly 25.29 cm.
In arithmetic, what is perimeter?The area around a form's edge is known as its perimeter. The perimeter of various forms can be calculated by summing the lengths of their sides.
Let's call the right triangle's shorter leg "x" for short.
The longer leg is then 5 cm longer than x, or x + 5, according to the situation.
The hypotenuse measures x + 10 cm longer than x.
By the Pythagorean theorem, we know that:
x² + (x+5)² = (x+10)²
Expanding and simplifying this equation gives:
2x² + 10x - 75 = 0
Dividing both sides by 2 gives:
x² + 5x - 37.5 = 0
We can find the value of x by using the quadratic formula:
x = (-5 ± sqrt(5² - 4(1)(-37.5))) / 2
x = (-5 ± sqrt(175)) / 2
x ≈ -8.68 or x ≈ 3.43
Since x represents a length, we must choose the positive solution x = 3.43 cm.
Therefore, the shorter leg of the triangle is 3.43 cm, the longer leg is 8.43 cm (3.43 + 5), and the hypotenuse is 13.43 cm (3.43 + 10). The perimeter of the triangle is the sum of the three sides, which is:
3.43 + 8.43 + 13.43 = 25.29 cm
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Suddeth Travel estimates that 80% of its employees have more than 12 days of unused sick leave. If 140 employees have more than 12 days of unused sick leave, how many employees work at the agency? A. 112 B. 164 C. 175 D. 700
Answer:
C) 175.
Step-by-step explanation:
Sure, here's a step-by-step solution:
Let's call the number of employees at the agency "x".
If 80% of the employees have more than 12 days of unused sick leave, that means 0.8 * x employees have more than 12 days of unused sick leave.
We know that 0.8 * x = 140, so we can solve for x by dividing both sides of the equation by 0.8:
x = 140 / 0.8
Simplifying, we get:
x = 175
So there are 175 employees who work at the agency, and the answer is C) 175.
Mary invests £12000 into a savings account. The account 1.5% compound interest per year. Work out the value of her investment after 2 years.
Answer:
Step-by-step explanation:
To calculate the compound interest on Mary's savings account, we can use the formula:
A = P * (1 + r/n)^(nt)
Where:
A is the amount after t years
P is the initial principal (£12000)
r is the interest rate (1.5%)
n is the number of times the interest is compounded in a year (let's assume it's compounded annually)
t is the number of years (2)
So, plugging in the values, we get:
A = £12000 * (1 + 0.015/1)^(1 * 2)
A = £12000 * (1.015)^2
A = £12000 * 1.0302
A = £12363.84
So, after 2 years, Mary's £12000 investment would be worth £12363.84, including the compound interest.
if f (x) equals 3 (x+4), find f (2)
Answer:
f(2) = 18
Step-by-step explanation:
If f(x) = 3 * (x + 4)
Than f(2) = 3 * (2 + 4) (coz x is an argument)
f(2) = 3 * (2 + 4)
f(2) = 3 * 6
f(2) = 18
Question 2 Part A:
An industrial copy machine has the ability to edit image dimensions by reducing it by a certain percentage
each time it copies. A design began with a length of 24 inches, represented by the point (0,24). After going
through the copy machine once, the length is 18, represented by the point (1,18).
Double click and enter the correct answer in the box by replacing the values of a and b.
f(x) = a(b)*
In the function, f(x) = a(b)ˣ the value of a and b is
a = 24b = 0.75How to find the value of a and bThe function defined by f(x) = a(b)ˣ is a exponential function
Where
a is the starting function
b is the base function
The starting function from (0,24)
24 = a(b)ˣ
a = 24
using (1, 18), we solve for the base
18 = 24(b)
b = 0.75
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Consider the system of equations.
y = -5x-1
y = 2x+6
Choose the correct answer to each question.
What is the slope of the first line?
What is the slope of the second line?
How many times do the lines intersect?
C
How many solutions does the system have?
C
How do I do these questions ??
As modeled, a movie is projected into a large outdoor screen. The bottom of the 60 foot-tall
Answer:
-
Step-by-step explanation:
the question isn't clear enough to answer it
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>
Which of the following tables of x- and y-values represents a function?
The tables of x- and y-values that represents a function include the following: C. table C.
What is a function?In Mathematics, a function is a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair in tables or relations.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (domain) to an output variable (range) representing a given scenario or situation such as the following:
x 1 3 7 5 2 4
y 6 6 6 6 6 6
In conclusion, we can reasonably infer and logically deduce that only table C represent a function.
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2. Sam spent $15 at an art store on paints, brushes, and paper. The paints cost $7.75 and the
brushes cost $3. Write and solve an equation you could use to find how much Sam spent on
paper.
Jim takes a counter at random from a bag containing 10 counters, numbered
1, 2, ..., 10.
Lyn throws an ordinary dice.
ind the probability that
Jim and Lyn both get a 3
The probability both get a 3 is 1/60
How to determine the probability both get 3From the question, we have the following parameters that can be used in our computation:
Jim = 1 to 10
Lyn = 1 to 6
Using the above as a guide, we have the following:
P(Jim = 3) = 1/10
P(Lyn= 3) = 1/6
Using the above as a guide, we have the following:
Required probability = 1/10 * 1/6
Evaluate the product
Required probability = 1/60
Hence, the probabilty is 1/60
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our jobs are to be done on four different machines. The cost in rupees of
producing ith on the jth machine is given below. Assign the jobs to different machines
so as to minimise the total cost.
Jobs
M1
M2
M3
M4
J1
15
11
13
15
J2
17
12
12
13
J3
14
15
10
14
J4
16
13
11
17
Given the functions f(x) = x3 + x2 – 2x + 3 and g(x) = log(x) + 2, what type of functions are f(x) and g(x)? Justify your answer. What key feature(s) do f(x) and g(x) have in common? (Consider domain, range, x-intercepts, and y-intercepts.)
The functions f(x) = x³ + x² - 2x + 3 and g(x) = log(x) + 2 have same range as (-∞,∞) or {y : y∈R}.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The given functions are -
f(x) = x³ + x² - 2x + 3
g(x) = log(x) + 2
The graph for function f(x) is plotted.
The function f(x) is a cubic function.
The domain for the function is (-∞,∞) or {x : x∈R}.
The range for the function is (-∞,∞) or {y : y∈R}.
The x-intercept for the function is (-2.37442376,0).
The y-intercept for the function is (0,3).
The graph for function g(x) is plotted.
The function g(x) is a logarithmic function.
The domain for the function is (0,∞) or {x : x>0}.
The range for the function is (-∞,∞) or {y : y∈R}.
The x-intercept for the function is (0.01,0).
The y-intercept for the function is not available.
Therefore, both functions have same range,
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Please help!! Due tomorrow morning!!
Directions: if QS represents an angle bisect or, solve for x.
(Ignore my answer)
The solution for x in the triangle is x = 52.5
How to solve for x in the triangle?
The bisector of an angle in a triangle divides the opposite side in the ratio of the sides containing the angle. That is:
PQ/QR = PS/SR
PQ = x, QR = 35, PS = 42 and SR = 70 - 42 = 28.
Therefore, we have:
PQ/QR = PS/SR
x/35 = 42/28
28*x = 42*35
28x = 1470
x = 1470/28
x = 52.5
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What is the Volume of the prism below
Answer:
140
Step-by-step explanation:
(5*7*8)/2= 280/2 =140
Find the total area of the shaded region. Ay 1.5- 14 x=5y3 (5,1) * = 5y? 0.5- х 07 0 2.5 5 7.5 Find the area of the region enclosed by the curves x= x = 7y?, x=0, and y=1. The area of the region enclosed by the curves is (Type a simplified fraction.)
The total area of the shaded region for the region x = 5y³ , x = 5y² in the interval ( 5, 1 ) is equal to ( 5 / 12 ).
From the attached graph :
The area of the shaded region :
x = 5y³ , x = 5y² for the interval ( 5, 1 ) is equal to :
= [tex]\int\limits^1_0 {( 5y^{2 } - 5y^{3 }}) \, dy[/tex]
= [ ( 5y³/3 ) - ( 5y⁴ / 4 ) ][tex]| \limits^1_0[/tex]
Substitute the lower limit and upper limit we get,
= (5 /3 )( 1 )³ - 0 - ( 5 / 4 )( 1⁴) + 0
= ( 5 / 3 ) - ( 5 / 4 )
= ( 20 - 15 ) / 12
= 5 / 12
Therefore, the total area of the shaded region in the given graph for the lower and upper limit is equal to ( 5 / 12 ) .
The given question is incomplete, I answer the question in general according to my knowledge:
Find the total area of the shaded region x = 5y³ , x = 5y² for the interval
( 5, 1 ).
Graph is attached.
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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 4.3 cubic feet of water weigh in pounds? In tons?
Answer:
268 pounds
Step-by-step explanation:
Two unit multipliers to be used for this unit conversion:
[tex]\frac{7.48 gallons}{1ft^{3}}[/tex] and [tex]\frac{8.33 pounds}{1 gallon}[/tex]
4.3 cubic feet = [tex](4.3ft^{3})[/tex]×[tex](\frac{7.48 gallons}{1ft^{3}})[/tex] ×[tex](\frac{8.33 pounds}{1ft^{3}})[/tex]
The cubic feet units in the numerator and denominator will cancel each other out. The gallons units in the numerator and denominator will cancel each other out.
= 268 pounds of water (Rounded to 3 significant figures)
Write a story that could represent this math problem. (2 points)
If John has 3 of 4 slices of pie, and Tom has 2 of 6 slices of pie, how many do they have all together?
I believe that is what type of story you needed, if wrong let me know.
Answer: Suppose Rita is trying to find the area of the carpet of 3/4 and 2/6 for a room of 4/4 sq to 6/6 sq with balcony of 1/4 and 4/6
Explanation: In the given rectangle fig. length is given 3/4 and breadth is given 2/6 for the whole rectangle is 4/4 to 6/6.
for each block length is given 1/4 and breadth is given 1/6. The darker shaded area represents the carpet of the above story.
The answer after multiplying it is 6/24 or 1/4.
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can someone pls give me the percent equation to these? 100 points to the fellow that does and brainiest if correct. Also pls hurry, its due today
6.5% of $400 is
what number?
12.5% of $100 is
what number?
130 is what percent
of 650?
$5.40 is what
percent of $4.50?
$8.40 is what
percent of $28?
56% of what
number is $21.84?
$495 is 55% of
what number?
120 is what percent
of 400?
4% of 975 is what
number?
Answer:
Step-by-step explanation:
You just need to remember to first convert percentages to decimal form by dividing the percent by 100. Then you can work out the calculations.
Also, remember that if the problem is asking you to find a percentage, you need to turn your decimal answer to a percentage by multiplying by 100.
I used x to represent what we are looking for:
6.5% of $400 = x
0.065 * 400 = $26
12.5% of 100 = x
0.125 * 100 = $12.5
x of 650 = 130
130/650 = 0.2 which equals 20%
x of $4.50 = $5.40
5.40/4.50 = 1.2 which equals 120%
x of $28 = $8.40
8.40/28 = 0.3 which equals 30%
56% of x = $21.84
21.84/0.56 = 39
55% of x = $495
495/0.55 = 900
x of 400 = 120
120/400 = 0.3 which equals 30%
4% of 975 = x
0.04 * 975 = 39
Answer:
See below
Step-by-step explanation:
a. 6.5% of $400:
[tex]= \frac{65}{100}[/tex]× ($400)
= $260
b. 12.5% of $100:
[tex]= \frac{12.5}{100}[/tex] × ($100)
= $12.5
c. 130 is what percent of 650:
[tex]=\frac{130}{650}[/tex]×100%
= 20%
d. $5.40 is what percent of $4.50:
[tex]= \frac{5.40}{4.50}[/tex]×100%
= 120%
e. $8.40 is what percent of $28:
[tex]= \frac{8.40}{28}[/tex]× 100%
= 30%
f. 56% of what number is $21.84:
=[tex]\frac{56}{100}[/tex]× number = $21.84
∴ Number = [tex]\frac{100}{56}[/tex]×$21.84
= $39
g. $495 is 55% of what number:
= $495 = [tex]\frac{55}{100}[/tex]× Number
∴Number = [tex]\frac{100}{55}[/tex]×($495)
= $900
h. 120 is what percent of 400:
= [tex]\frac{120}{400}[/tex]×100%
= 30%
i. 4% of 975 is what number:
= [tex]\frac{4}{100}[/tex]×975
= 39
Simplify the following expression using rational exponents. Assume all variables are positive.
(4y2/5)^2
A reasonable exponent is one that is fractional. For instance, 412 4 1 2 can be used to represent the number 4.
What is meant by rational exponent?Exponents that are fractions with the denominator a root and the numerator a power are known as rational exponents. For instance, 813 is another method to write 38, while 1612 is another way to write 16. A fractional exponent is a rational exponent. For instance, the number 4 can be written as 412 4 1 2. Though they can be challenging to use at first, rational exponents can actually make some issues simpler.The ability to express rational exponents in pq form as opposed to irrational exponents in pq form is one of the key distinctions between the two types of exponents. Rational exponents are rational numbers, whereas irrational exponents are infinite or non-repeating decimals.Given,
[tex]$\left(\frac{4 y^2}{5}\right)^2[/tex]
Apply exponent rule: [tex]$\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$[/tex]
[tex]$=\frac{\left(4 y^2\right)^2}{5^2}[/tex]
Simplify [tex]$\left(4 y^2\right)^2: 16 y^4$[/tex]
[tex]$=\frac{16 y^4}{5^2}[/tex]
The we get,
[tex]$& =\frac{16 y^4}{25}[/tex]
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In the diagram, RSTU~ ABCD. Find the ratio of their perimeters.
U
R
18 S
36
T
D
A
24
The ratio of their perimeters is
B
C
Answer: Let's call the ratio of the perimeters of the two similar figures "k". That means that for every unit of length in RSTU, there are k units of length in ABCD.
Since UR = 18 and DA = 24, k = 24/18 = 4/3.
So for every length in RSTU, there are 4/3 times that length in ABCD. We can use this ratio to find the corresponding lengths in ABCD. For example, SR = 36, so BS = 36 * (4/3) = 48.
Now that we have the lengths of all sides of ABCD, we can find its perimeter:
Perimeter of ABCD = 24 + 48 + BC + 24 = 120 + BC
Perimeter of RSTU = 18 + 36 + 18 + 36 = 108
So the ratio of their perimeters is:
Perimeter of ABCD / Perimeter of RSTU = (120 + BC) / 108 = (120 / 108) + (BC / 108) = 20/18 + BC/108
Since the perimeters of the two figures are similar, the ratio of their perimeters is equal to the ratio of their corresponding side lengths:
20/18 + BC/108 = 4/3
Solving for BC:
BC = (4/3 - 20/18) * 108 = 36
Step-by-step explanation:
13. Interpret the IQR and median in the context of the data set.
The interquartile range is 4 and the median is 27.
What is the interquartile range?The interquartile range is the difference between the third quartile and the first quartile. On a box plot, the interquartile range is the difference between the first line and the third line on the box.
Interquartile range = 28 - 24 =4
Median is the central value of a data set. On a box plot, the median is the second line on the box.
The median is 27.
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PLEASE HELP ME ASAP
5. The first row of a stem-and-leaf chart appears as follows: 62 | 1 3 3 7 9. Assume whole
number values.
a. What is the "possible range" of the values in this row?
b. How many data values are in this row?
c. List the actual values in this row of data.
I need the first one
Answer:
∠1 = ∠2 = 135
Step-by-step explanation:
We know that the sum of the interior angles of a polygon of n sides = (n – 2) × 180° = 3 x 180°= 540°. Hence, the sum of interior angles of a pentagon is 540°.
so ∠1 + ∠2 + 3(90°) = 540°
since ∠1 = ∠2
∠1 + ∠1 + 3(90) = 540
2∠1 + 270 = 540
2∠1 = 540 - 270
2∠1 = 270
∠1 = 270/2 = 135
Can someone help me with the step by step solutions to these? Thanks
Answer:
c. √2/30
f. 13√3/14
i. -11√10/24
Step-by-step explanation:
You want the sums of the fractions shown.
Sum of fractionsTwo fractions can be added like this:
[tex]\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}[/tex]
If the denominators have a common factor (k), then this can be reduced to ...
[tex]\dfrac{a}{bk}+\dfrac{c}{dk}=\dfrac{ad+bc}{bdk}[/tex]
The product bdk is the least common denominator when k is the greatest common factor.
Here, the numerators have a common factor, so we can factor that out, perform the sum, then multiply the result by that numerator factor.
c[tex]\dfrac{\sqrt{2}}{5}-\dfrac{\sqrt{2}}{6}=\sqrt{2}\left(\dfrac{1}{5}-\dfrac{1}{6}\right)=\sqrt{2}\cdot\dfrac{6-5}{5\cdot6}=\boxed{\dfrac{\sqrt{2}}{30}}[/tex]
f[tex]\dfrac{3\sqrt{3}}{7}+\dfrac{\sqrt{3}}{2}=\sqrt{3}\left(\dfrac{3}{7}+\dfrac{1}{2}\right)=\sqrt{3}\cdot\dfrac{3\cdot2+7}{7\cdot2}=\boxed{\dfrac{13\sqrt{3}}{14}}[/tex]
iThe denominators have a common factor of 2: 6=3·2, 8=4·2.
[tex]\dfrac{-5\sqrt{10}}{6}+\dfrac{3\sqrt{10}}{8}=\sqrt{10}\left(\dfrac{-5}{6}+\dfrac{3}{8}\right)=\sqrt{10}\cdot\dfrac{-5\cdot4+3\cdot3}{3\cdot4\cdot2}=\boxed{-\dfrac{11\sqrt{10}}{24}}[/tex]
Write the following comparison as a ratio reduced to lowest terms. 7 nickels to 47 dimes
7 nickels is 7/5, thus 7 nickels to 47 dime is 1.4 dime to 47 dime.
When both terms are multiplied by their biggest common factor, 1.4 dime, the ratio can be simplified to its simplest form: 47 dimes = 14: 470
What is the ratio?The ratio of quantity, amount, or size of two or more items is known as proportion. It is the indicated quotient of two mathematical expressions.
As a ratio, what is 1 to 2?"1 to 2" is the way to write the ratio 1: 2. Accordingly, of the total of 3, there is one component that is worth 1 and another part that is worth 2. Changing a part-to-part ratio to a fraction To get the whole, add the ratio terms. The denominator should be this.
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Find the volume to each equation
(Directions listed above questions)
The volume of the cube is 444.19 in³
The volume of the rectangular prism is 661.2 ft³
The volume of the triangular prism is 30.04 yd³
The volume of the cylinder is 380.57 km³
How to find the volumeVolume of a cube is solved using the formula
= length³
= 7.63³
= 444.19 in³
Volume of a rectangular prism is solved using the formula
= Area of base * height
= 9.5 * 8.7 * 8
= 661.2 ft³
Volume of a triangular prism is solved using the formula
= 1/2 × base × height × length
= 1/2 * 5.84 * 3.08 * 3.34
= 30.04 yd³
Volume of a cylinder is solved using the formula
= π * radius² * height
= π * 3² * 13.46
= 380.57 km³
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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
