As a bowling instructor, you calculate your students' averages during tournaments. In 5 games, one bowler had the following scores: 143, 156, 172, 133, and 167. What was that bowler's average?
Answer:
154.2
Step-by-step explanation:
143 plus
156 plus
172 plus
133 plus
167 = 771
divide by 5 equals 154.2
The Mogul Runners ski club planned a trip to Park City. Of the total number of club members, 11 signed up to go. If this is 25% of the club, how many members does the ski club have?
Answer: 44
Step-by-step explanation: Since 11 members are equal to 25% of the club, 11 members is 1/4 of the club because 25% = 1/4. There are four-fourths in a whole so 11x4 = 44 members. The ski club has 44 members.
A bookstore charges $4 for shipping, no matter how many books you buy. Irena makes a graph showing the shipping cost for I to 5 books. She claims that the points she graphed lie on a line. Does her statement make sense? Explain
Answer:
can we see the graph?
Step-by-step explanation:
3
Find seven ordered pairs for the equation y=x + 6 using the given values of x. Then
determine its graph.
y
-3 1
x
***
...
The seven ordered pairs that fit on the axes of the graph include the following:
Ordered pair = (0, 6).Ordered pair = (-3, -21).Ordered pair = (-1, 5).Ordered pair = (2, 14).Ordered pair = (1, 7).Ordered pair = (-2, -2).Ordered pair = (-4, -58).How to complete the table?In order to use the given polynomial function to complete the table, we would have to substitute each of the values of x (x-values) into the polynomial function and then evaluate as follows;
When the value of x = -3, the output value of this polynomial function is given by;
y = x³ + 6
y = (-3)³ + 6
y = -27 + 6
y = -21
By observing critically the graph (see attachment), we can logically deduce that it represents a polynomial function.
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Highschool geometry please answer questions 8-10 in the attachment added
the Track Club from the 50 yard – how many inches do they run
Answer:
1800 inches
Step-by-step explanation:
A yard is a unit of length equal to 3 feet or exactly 0.9144 meters
An inch is a unit of length equal to exactly 2.54 centimeters. There are 12 inches in a foot, and 36 inches in a yard.
Given the graph of a function f(x). What is f(-4)?
Answer:
f (k)
Step-by-step explanation:
Here, we are required to determine the value of f(-4) given the graph of a function f(x) as in the attached image.
The value of f(-4) given the graph of the function f(x) as in the attached image is; f(-4) = 2.The graph of the function f(x) is a curve, where x is the independent variable and f(x) is dependent on the value of x.
By observation, each box on the represents 1 unit on the x- and f(x) axis.
Ultimately, the point f(x) which corresponds to the point where x = -4 is; f(-4) = 2.
Therefore, f(-4) = 2 according to the graph of the function f(x) as given in the attached image.
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solve for w 12=9w-5w
Answer:
answer is w= 3
Step-by-step explanation:
12=9w-5w
12=4w
w= 12/4
w= 3
Answer:
w=3
Step-by-step explanation:
1. 12=9w-5w
2. 12=4w
3. 12/4=4w/4
4. w=3
Which graph is that of the inequality shown below ?
Answer:
C
Step-by-step explanation:
y <= 2x - 2
the delimiter line is therefore
y = 2x - 2
that is true for all 4 answer options.
but the y-values must be smaller than the values in the line. so, the area right-down from the line is correct.
that leaves us with B and C.
dotted line or solid line - the difference is if the line values are included in the solution or excluded.
if the line is dotted, then the line is not included.
if the line is solid, then the line is included.
because the inequality uses "<=", the line is included.
so, the answer with the solid line is correct : C.
A polynomial function g(x) has a positive leading coefficient. Certain values of g(x) are given in the following table. x –4 –1 0 1 5 8 12 g(x) 0 3 1 2 0 –3 0 If every x-intercept of g(x) is shown in the table and each has a multiplicity of one, what is the end behavior of g(x)?
Using the Factor Theorem and limits, the end behavior of g(x) is that the function decreases to the left and increases to the right.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots \(x_1, x_2, \codts, x_n\) is given by:
\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)
In which a is the leading coefficient.
Considering the table, the roots are given as follows:
\(x_1 = -4, x_2 = 5, x_3 = 12\)
Hence the function is:
f(x) = a(x + 4)(x - 5)(x - 12).
f(x) = a(x² - x - 20)(x - 12)
f(x) = a(x³ - 13x² - 32x + 240).
When x = 0, y = 1, hence the leading coefficient is found as follows:
240a = 1
a = 0.004167
Then:
f(x) = 0.004167(x³ - 13x² - 32x + 240).
The end behavior is given by the limits of f(x) as x goes to infinity, hence:
\(\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 0.004167 x^3 = -\infty\).\(\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 0.004167 x^3 = \infty\).Hence the end behavior is that the function decreases to the left and increases to the right.
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-8x+y=6
-8x+3y=-14
How would you solve this using the elimination method? Thanks!
Answer:
x = -1,375
y = -5
Step-by-step explanation:
{-8x + y = 6, / : (-1)
{-8x + 3y = -14;
Multiply the first equation by -1, so that we could eliminate 8x:
+ {8x - y = -6,
{-8x + 3y = -14;
----------------------
4y = - 20 / : 4
y = -5
Now, make x the subject from the first equation (you can do it from the 2nd one instead):
8x = -6 + y / : 8
x = -0,75 + 0,125y
x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375
The graph of the function rule that models the volume of the sphere has symmetry with respect to ____?
The correct option D: the origin, has the symmetry of the volume of sphere for the graph of the function rule.
Explain the term symmetry along origin?About the Origin: Symmetry. If a point appears on a graph at every time, then the graph is symmetric having respect to the origin. When seen in relation to the origin, this graph is symmetric.A function having a single term which is the sum of a real number, the coefficient, as well as a variable raised to something like a fixed real number is called a power function. (A coefficient is a number which multiplies a variable by an exponent.) Think of equations like area or volume as an illustration.For the stated question.
The volume of the sphere is modeled by the power function with respect to the radius as;
V = f(r) = 4/3πr³
As, r is independent of any of the coordinate axis.
Thus, the function rule's graph, which describes the volume of the sphere, is symmetric with regard to the origin.
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In a survey of thousands of college students, 46% of the respondents reported falling asleep in class due to poor sleep. You randomly sample 10 students in your dorm and eight state that they fell asleep in class during the last week due to poor sleep.
Find the probability that at least 8 students of the 10 fell asleep in class last week.
Using the binomial probability relation ; the probability that atleast 8 students fell sleep in the class is 0.0317
Using the binomial probability relation :
P(x = x) = nCx * p^x * q^(n-x) p = probability of success = 46% = 0.46q = 1 - p = 0.54n = number of trials = 10P(x ≥ 8) = p(x = 8) + p(x = 9) + p(x = 10)
Using a binomial probability calculator :
P(x ≥ 8) = 0.0263 + 0.00498 + 0.00042
P(x ≥ 8) = 0.0317
Therefore, the probability that atleast 8 of the students fell asleep is 0.0317
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Pablo solved the polynomial equations given in the table. Determine whether each polynomial is correct. Select Correct or Incorrect for each equation.
Equation
(b²+7b-9)+(4b-6b²) = -8b² + 14b-9
(4a+6)-(3a²-9a+1)=-3a²+ 13a +5
(12c-8c²)+(5c²- 10c) = -3c²+2c
The first equation is incorrect.
The second equation is correct.
The third equation is correct.
Let's go through each equation and determine whether it is correct or incorrect:
(b²+7b-9)+(4b-6b²) = -8b² + 14b-9
To determine if this equation is correct, we need to simplify both sides and check if they are equal.
On the left side:
(b²+7b-9)+(4b-6b²) = b² - 6b² + 7b + 4b - 9 = -5b² + 11b - 9
On the right side:
-8b² + 14b - 9
Comparing both sides, we can see that -5b² + 11b - 9 is not equal to -8b² + 14b - 9. Therefore, the equation is incorrect.
(4a+6)-(3a²-9a+1)=-3a²+ 13a +5
Again, we need to simplify both sides of the equation and check if they are equal.
On the left side:
(4a+6)-(3a²-9a+1) = 4a + 6 - 3a² + 9a - 1 = -3a² + 13a + 5
On the right side:
-3a² + 13a + 5
Comparing both sides, we can see that -3a² + 13a + 5 is equal to -3a² + 13a + 5. Therefore, the equation is correct.
(12c-8c²)+(5c²- 10c) = -3c²+2c
Again, let's simplify both sides and compare them.
On the left side:
(12c-8c²)+(5c²- 10c) = 12c - 8c² + 5c² - 10c = -3c² + 2c
On the right side:
-3c² + 2c
Comparing both sides, we can see that -3c² + 2c is equal to -3c² + 2c. Therefore, the equation is correct.
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The value of a coin in 2010 was $40. The value of the coin has increased in value at a rate of 16.9% annually.
What was the value of the coin in 2019?
Enter your answer in the box rounded to the nearest dollar.
The value of the coin in 2019 would be approximately $132.
To calculate the value of the coin in 2019, we need to consider the annual increase rate of 16.9% from 2010 to 2019. We can use the compound interest formula to find the final value.
Starting with the initial value of $40 in 2010, we can calculate the value in 2019 as follows:
Value in 2019 = Initial value * (1 + Rate)^n
where Rate is the annual increase rate and n is the number of years between 2010 and 2019.
Plugging in the values:
Value in 2019 = $40 * (1 + 0.169)^9
Value in 2019 ≈ $40 * 2.996
Value in 2019 ≈ $119.84
Rounding the value to the nearest dollar, we get approximately $120. Therefore, the value of the coin in 2019 would be approximately $120.
However, please note that the exact value may vary depending on the specific compounding method and rounding conventions used.
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Based on the survey results, which is true about the t-shirts Mrs. Hanson should order?
Mrs. Hanson should order equal numbers of each type of shirt.
Mrs. Hanson should order about 2.5 times as many crew neck shirts as raglan shirts.
Less than 25% of Mrs. Hanson's order should be polo shirts.
Mrs. Hanson should order 50% fewer v-neck shirts than polo shirts.
Answer:
Mrs. Hanson should order about 2.5 times as many crew neck shirts as raglan shirts.
Step-by-step explanation:
Answer:
Mrs. Hanson should order about 2.5 times as many crew neck shirts as raglan shirts.
Step-by-step explanation:
Solve X^2 - 6x = -5 by completing the square. Show all work for the steps below. A) For x^2 - 6x + c = -5 + c, what value of c is used to complete the square? B) Substitute the value for c in Part 2(a). Then complete the square to rewrite the equation as the square of a binomial. C) Solve for x. ( Will Mark Brainliest but no links or nonsense answers please) I Also Posted A Picture Of The Question And Steps so you can see what the question and steps are to take.
Answer:
Below.
Step-by-step explanation:
x^2 - 6x = -5
x^2 - 6x + 9 = -5 + 9 c = 9
(x - 3)^2 = 4
x - 3 = +/- sqrt4
x - 3 = +/- 4
x - 3 = 2 gives x = 5 and
x - 3 = -4 gives x = -1.
PRE-CALC
khalid invests $500 in an account that earns 1.5% interest per year, compounded annually. Which of the following is formed by the amount in his account from year to year?
an arithmetic series
an arithmetic sequence
a geometric series
a geometric sequence
For your question: "Khalid invests $500 in an account that earns 1.5% interest per year, compounded annually. Which of the following is
formed by the amount in his account from year to year?"
The geometric sequence is formed.
Answer:
d
Step-by-step explanation:
Refer to the information below to answer Questions 9 and 10. Value of Property Up to K35 000 K35 000 to K70 000 K70 000 to K140 000 Over K140 000 10. Rate of Stamp Duty 2% 3% 4% 5% 9. Calculate the stamp duty payable on properties whose purchase price is K45 000. (1 mark) Answer: Calculate the stamp duty payable on properties whose purchase price is K150 000. (1 mark) Answer:
9. The stamp duty payable on a property with a purchase price of K45,000 is K1,350.
10. The stamp duty payable on a property with a purchase price of K150,000 is K7,500.
To calculate the stamp duty payable on properties with a purchase price of K45,000 and K150,000, we need to apply the corresponding rates of stamp duty based on the given information.
Given:
Value of Property:
Up to K35,000: Stamp Duty Rate - 2%
K35,000 to K70,000: Stamp Duty Rate - 3%
K70,000 to K140,000: Stamp Duty Rate - 4%
Over K140,000: Stamp Duty Rate - 5%
9. Calculate the stamp duty payable on properties whose purchase price is K45,000:
Since the purchase price of K45,000 falls within the range of K35,000 to K70,000, the stamp duty rate applicable is 3%.
Stamp Duty Payable = Purchase Price * Stamp Duty Rate
= K45,000 * 3%
= K45,000 * 0.03
= K1,350
Therefore, the stamp duty payable on a property with a purchase price of K45,000 is K1,350.
10. Calculate the stamp duty payable on properties whose purchase price is K150,000:
Since the purchase price of K150,000 is above K140,000, the stamp duty rate applicable is 5%.
Stamp Duty Payable = Purchase Price * Stamp Duty Rate
= K150,000 * 5%
= K150,000 * 0.05
= K7,500
Therefore, the stamp duty payable on a property with a purchase price of K150,000 is K7,500.
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How do you do this question?
Part 1
\(x = g(y), \ c \le y \le d\\\\\\x = 3+4y^2, \ 1 \le y \le 2\\\\\\\frac{dx}{dy} = 8y, \ 1 \le y \le 2\\\\\\\displaystyle A = 2\pi \int_{c}^{d}y\sqrt{1+[g'(y)]^2}dy\\\\\\\displaystyle A = 2\pi \int_{c}^{d}y\sqrt{1+\left[\frac{dx}{dy}\right]^2}dy\\\\\\\displaystyle A = 2\pi \int_{1}^{2}y\sqrt{1+(8y)^2}dy\\\\\\\displaystyle A = 2\pi \int_{1}^{2}y\sqrt{1+64y^2}dy\\\\\\\displaystyle A = 2\pi \int_{1}^{2}\sqrt{1+64y^2}*ydy\\\\\\\displaystyle A = 2\pi \int_{65}^{257}\sqrt{u}*\frac{du}{128}\\\\\\\)
In the last two steps I let u = 1+64y^2, so du/dy = 128y which leads to ydy = du/128.
Note the change in the limits of integration. If y = 1, then u = 1+64y^2 = 65. If y = 2, then 1+64y^2 = 257
----------------------------
Part 2
\(\displaystyle A = 2\pi \int_{65}^{257}\sqrt{u}*\frac{du}{128}\\\\\\\displaystyle A = 2\pi*\frac{1}{128}\int_{65}^{257}u^{1/2}*du\\\\\\\displaystyle A = \frac{\pi}{64}\int_{65}^{257}u^{1/2}*du\\\\\\\displaystyle A = \frac{\pi}{64}\left(\frac{2}{3}u^{3/2}+C\right)\Bigg]_{65}^{257}\\\\\\\displaystyle A = \frac{\pi}{64}\left(\left(\frac{2}{3}(257)^{3/2}+C\right)-\left(\frac{2}{3}(65)^{3/2}+C\right)\right)\\\\\\\displaystyle A = \frac{\pi}{64}*\frac{2}{3}\left((257)^{3/2}-(65)^{3/2}\right)\\\\\\\)
----------------------------
Part 3
\(\displaystyle A = \frac{\pi}{96}\left(\sqrt{257^3}-\sqrt{65^3}\right)\\\\\\\displaystyle A = \frac{\pi}{96}\left(\sqrt{257^2*257}-\sqrt{65^2*65}\right)\\\\\\\displaystyle A = \frac{\pi}{96}\left(\sqrt{257^2}*\sqrt{257}-\sqrt{65^2}*\sqrt{65}\right)\\\\\\\displaystyle A = \frac{\pi}{96}\left(257\sqrt{257}-65\sqrt{65}\right)\\\\\\\)
\(\displaystyle A = \frac{\pi}{96}*257\sqrt{257}-\frac{\pi}{96}*65\sqrt{65}\\\\\\\displaystyle A = \frac{257\pi\sqrt{257}}{96}-\frac{65\pi\sqrt{65}}{96}\\\\\\\displaystyle A = \frac{-65\sqrt{65}\pi}{96}+\frac{257\sqrt{257}\pi}{96}\\\\\\\)
Select the best choice to correct the vague pronoun reference in this sentence.
Did you see it in the sky last night?
in the evening
looking up
near the stars
the spaceship
The vague pronoun "it" can be replaced by -
Option D: the spaceship
What is a pronoun?
An alternative to a noun is a pronoun. In order to avoid using the noun more than once in a paragraph or piece of writing, it replaces. Singular and plural pronouns can be used. The verb in the sentence should be utilised in keeping with the specific pronoun form that is being employed.
The sentence is "Did you see it in the sky last night?".
"The spaceship" is the most appropriate option to replace the ambiguous pronoun reference in this statement.
Did you see it in the sky last night? is a vague question because "it" could refer to a variety of sky-observed objects.
The language becomes clearer and more precise by swapping "it" for "the spaceship," referring specifically to a particular item observed in the sky.
Therefore, the spaceship is the correct choice.
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Find the area of the object.
140cm table
Answer: 15,393.8cm²
Step-by-step explanation:
Using the formulas
A=πr2
d=2r
Solving for A
A=1/4π d2=1/4·π·1402
≈ 15393.804cm²
Brainliest me please if right! <3pls help and explain how you got the answer
The class of the equation and the cross section equation are;
The equation is a hyperboloid of two sheets
The cross sections are;
Equation at z = 0 is; y²/8 - x²/8 = 1
Equation at y = -4 is; x²/8 + z² = 1
Equation at y = 0 is; x²/8 + z² = -1
Equation at y = 4 is; x²/8 + z² = 1
Equation at x = 0 is; y²/8 - z² = 1
What is an equation ?An equation is a mathematical statement which indicates the equivalence two expressions by joining them with the '=' sign.
The equation can be presented as follows;
y² = x² + 8·z² + 8
y² - x² - 8·z² = 8
y²/8 - x²/8 - z² = 1
The above equation is the equation of an hyperboloid of two sheets, where;
a² = 8, b² = 1, and c² = 8
Please find attached the diagram of the surface, created with an online 3D graphing tool.
The equation for the cross section at z = 0, can be obtained by plugging in z = 0, into the equation as follows;
y²/8 - x²/8 - 0 = 1
y²/8 - x²/8 = 1
The above equation is the equation of an hyperbola in the xy plane
The equation for the cross section at y = -4, can be obtained by plugging in y = -4, into the equation as follows;
4²/8 - x²/8 - z² = 1
- x²/8 - z² = 1 - 4²/8 = -1
- x²/8 - z² = -1
x²/8 + z² = 1
The above is an equation of an ellipse in the xz plane
The equation for the cross section at y = 0, can be obtained by plugging in y = 0, into the equation as follows;
0²/8 - x²/8 - z² = 1
- x²/8 - z² = 1
Therefore; x²/8 + z² = -1
The equation for the cross section at y = 4, can be obtained by plugging in y = 4, into the equation as follows;
4²/8 - x²/8 - z² = 1
- x²/8 - z² = 1 - 2 = -1
x²/8 + z² = 1
The above equation is the equation of an ellipse in the xz plane
The equation for the cross section at x = 0, can be obtained by plugging in x = 0, into the equation as follows;
y²/8 - 0²/8 - z² = 1
y²/8 - z² = 1
The equation is the equation of an hyperbola in the yz plane
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help me pls I don't get what to do
37 and 1/2 % of 104?
37 and 1/2 % of 104 is 39 .
Given,
37 and 1/2 % of 104
Simplifying further,
Convert mixed fraction into simple fraction,
37 and 1/2 % = 75/2%
Now,
75/2% of 104
= 75/2 ×1/100×104
=39 .
Hence 39 is the required answer.
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Determine whether angle-angle-angle (AAA) is a valid means for establishing triangle congruence. If it is a valid criterion, explain why. If it is not valid, use GeoGebra to create a counterexample demonstrating that it doesn't work and give an explanation. If you construct a counterexample, take a screenshot of your work, save it, and insert the image in the space below. !! I just write in a box!!
A triangle is a fundamental form in geometry. The AAA property can not be used to prove if the triangles are congruent.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.
The property angle-angle-angle (AAA), is used for similar triangles. It can not be used to prove that two triangles are congruent triangles. Therefore, it is not a valid criterion.
Now, this can be proved using two triangles having the same angle measurement as 60°. The two triangles given below has the same angle measurement although, their sides have different measurement, thus, the two triangles are not equal.
Hence, the AAA property can not be used to prove if the triangles are congruent.
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Answer: A triangle is a basic geometric shape. Triangle congruence cannot be established using the AAA property. A triangle is a polygon having three vertices and three edges. It is a fundamental geometric figure. For comparable triangles, the property angle-angle-angle (AAA) is employed. It cannot be used to establish the congruence of two triangles. As a result, it is an invalid standard. Now, this may be demonstrated using two triangles with angles equal to or greater than 60°. The two triangles shown below are not equal because they have different side measurements despite having the same angle measurement. The triangles' congruence cannot therefore be established using the AAA property.
Step-by-step explanation:
3. Solve 1 < 3x – 2 < 13.
Answer:
1< x <5
Step-by-step explanation:
1<3x−2<13
1+2<3x−2+2<13+2 (Add 2 to all parts)
3<3x<15
33<3x3<153 (Divide all parts by 3)
1< x <5
Answer:
(1,5)
Step-by-step explanation:
Maximize
z
=
5
x
+
y
Subject to
2
x
+
6
y
≤
54
7
x
+
3
y
≤
63
x
≥
0
y
≥
0
Maximum is
at
x
=
y
=
Therefore , the solution of the given problem of linear equation comes out to be its maximum when x=30 and y=20. The top number is 410.
A linear equation is precisely what?A straightforward regression curve is created using the equation y=mx+b. The y-intercept is m, and the slope is B. The preceding line is commonly referred to as an "mathematical formula blending many variables" even if y or y represent independent components. Only two variables are present in bivariate linear equations. There are no known solutions to application issues involving linear equations. The formula Y=mx+b, that is also expressed as mx+b, denotes a straightforward system of equations.
Here,
The LPP given is:
Maximize 7x+10y subject to contsraints
4x+6y ≤ 240 ⇒2x+3y ≤ 120
6x+3y ≤ 240⇒2x+y ≤ 80
x≥10
y≥0
Visualize the graphs of x=10, 2x+3y=120, and x+y=80. The area of the solution that is viable is indicated by the shading.
The feasible region's corner points are (10, 0), (40, 0), (30, 20), and (10, 100/3)
The figures show that 7x+10y is at its maximum when x=30 and y=20. The top number is 410.
Therefore , the solution of the given problem of linear equation comes out to be its maximum when x=30 and y=20. The top number is 410.
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The complete question is "Solve the following linear programming problem graphically:
Maximize Z=7x+10y
subject to the constraints
4x+6y≤240
6x+3y≤240
x≥10
x≥0,y≥0"
A display case is shaped like the prism shown below. The bases are right triangles. Find the surface area of the prism.
Answer:
200ft²
Step-by-step explanation:
SA = 8(15) + (8+15+17) 20
= 120+ (4)(20)
= 120+80
= 200ft²
Panat has assets that total $9,500. His liabilities total $1,900. Which expression will find Patrick's net worth?
$9.500-$1.900
$1.900-$9.500
$1.900-$9.500
$9.500-$1.900
Helppp
Answer:
D
Step-by-step explanation:
assets total - liabilities/deductions = net worth
his income is what his net worth it, but liabilities is what you dont have. its what you owe/need to pay/dont own. subtracting these two will give you your real net wroth.
The correct expression to find Patrick's net worth is D: $9,500 - $1,900.
What is the net worth?The difference between an individual's assets and liabilities is described as net worth.
As per the question, Patrick's assets are given as $9,500 and his liabilities are given as $1,900.
To find his net worth, we need to subtract his liabilities from his assets.
Thus, the expression for Patrick's net worth is:
Net worth = Assets - Liabilities
Net worth = $9,500 - $1,900
Net worth = $7,600
Therefore, Patrick's net worth is $7,600.
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