2. Avea checked out 18 books
from the library. Half of them
are nonfiction. How many
nonfiction books did she check
out?

Answers

Answer 1
Solution -

18 Total books
Half of 18 is 9
(18 divided by 2)
So Avea checked out 9 nonfiction books
Answer 2

Answer: she checked out 9 nonfiction books

Step-by-step explanation:

18-9=9


Related Questions

Which of the following points best represents the location of -1;
15.
ос
OD
Ов
ОА
+
-2
в с
0
on the number line?
D
2 +
2

Answers

A because u start from the -1 going backwards and where point A is just makes sense

I need help, I know it gave me the answer but I don’t understand how it got (-3) someone explain please

Answers

Answer: h=14

Step-by-step explanation:

If x=-18, then

h=17+(-18)/6

h=17+(-3)

h=17-3

h=14

Answer:

Step-by-step explanation:

so, the calculation was :  h = 17 + [tex]\frac{-18}{6\\}[/tex]

To subtract "[tex]\frac{-18}{6}[/tex] " we need to make it the same denominator  as "17"

(it's not written but technically 17 = [tex]\frac{17}{1}[/tex] )

Yet, we see that [tex]\frac{-18}{6} =\frac{-3* 6}{1*6}[/tex]

We just need to remove both the 6 that are not useful here and :

[tex]\frac{-3*6}{1*6} =\frac{-3}{1}= -3[/tex]

We obtain h = 17 - 3 = 14

hope it helped :)

The distribution of the amount of money undergraduate students spends on books for a term is slightly right-skewed, with a mean of $400 and a standard deviation of S80. If a simple random sample of 100 undergraduate students is selected, what is the probability that these students spend, on average, more than $425 on books?

Answers

The probability that on average these students spend more than $425 on books is given as follows:

0.0009 = 0.09%.

How to obtain the probability using the normal distribution?

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

The parameters for this problem are given as follows:

[tex]\mu = 400, \sigma = 80, n = 100, s = \frac{80}{\sqrt{100}} = 8[/tex]

The desired probability is one subtracted by the p-value of Z when X = 425, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{425 - 400}{8}[/tex]

Z = 3.125.

Z = 3.125 has a p-value of 0.9991.

1 - 0.9991 = 0.0009 = 0.09%.

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Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. The total cost in dollars for ordering 5 tickets is $108.00. Which linear function represents c, the total cost, when x tickets are ordered? (A service fee is a single fee applied to the total, no matter the number of tickets purchased).

Answers

Considering the definition of a line, the linear function that represents the total cost when x tickets are ordered is c= 20.5x + 5.50.

What is a linear equation

A linear equation o line can be expressed in the form y = mx + b

where

x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.

Total cost in this case

In this case, you know:

Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. This is, as service fee is a single fee applied to the total, no matter the number of tickets purchased, the value of "b" is 5.50.The total cost in dollars for ordering 5 tickets is $108.00

Being Total cost= set price per ticket× amount of tickets + 5.50, then:

108=set price per ticket× 5 + 5.50

108 - 5.50= set price per ticket× 5

102.5= set price per ticket× 5

102.5÷5= set price per ticket

20.5= set price per ticket

Finally, the total cost is Total cost= 20.5× amount of tickets + 5.50.

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Answer:

Its letter A

Step-by-step explanation:

compare the function rule f(x) = 3x +2 and the graph of g(x)

which statements are true? select two that apply.
-g(x) increases at a faster rate over the interval (-1,0)
-g(x) increases at a faster rate over the interval (1,2)
-g(x) increases at a faster rate over the interval (0,1)
-f(x) increases at a faster rate over the interval (2,3)
-f(x) increases at a faster rate over the interval (0,1)
-f(x) increases at a faster rate over the interval (1,2)

Answers

On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .

What is graphs?

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

by graphs of the function f (x) and g( x)

[tex]lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5[/tex]

from the graphs n f (x) and g( x) are 1 and 5 .

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A line passes through the origin (−1, 1) and (4, n). Find the value of n.

Answers

The line y = - x has a coordinate value of (4, - 4) passing through the origin.

What are lines and their slopes?

We know lines have various types of equations, the general type is

Ax + By + c = 0, and equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, A line passes through the origin, (−1, 1) and (4, n).

So, The slope of the line is,

m = (1 - 0)/(- 1 - 0).

m = - 1.

Now,

1 = -1(-1) + b.

b = 0.

y = - x.

At x = 4,

y = - 4.

So, The point (4, n) is (4, - 4).

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3a+14b

I'm not good at math, it's my weakest subject

Answers

On solving the question, we can say that y using the given information we can prove that similar angle m ∠ABC = m ∠EDC.

What are similar angles?

Polygons' corresponding sides and corresponding angles are compared as part of the geometric tests for congruence and similarity. With care taken to maintain the order of adjacency, each side and each angle in one polygon is paired with a side or angle in the other polygon in these tests.

Given:

m ∠1 = m ∠2

m ∠2 = m ∠4

We have to prove that m ∠ABC = m ∠EDC

∠EDC = ∠3 + ∠4

m ∠ABC = m ∠1 + m ∠2

m ∠EDC = m ∠3 + m ∠4

m ∠1 + m ∠2 = m ∠3 + m ∠4      

m ∠ABC = m ∠EDC

Hence, by using the given information we can prove that  

m ∠ABC = m ∠EDC.

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In the construction of bridges, engineers use a formula to help
determine the allowable stress on a bridge rocker, a component of the
bridge that handles the stress and weight placed on the pavement of the
bridge. The engineers use the formula F =11/300d (F − 13), where F is the
strength of the steel in kilopound per square inch and d is the diameter
of the rocker in millimeters.
Solve the formula F =11/300d (F − 13) for d.

Answers

From the engineers formula given, making d the subject of the formula gives us; d = 300F/(11(F - 13))

How to change the subject of the formula?

We are given the engineers formula as;

F = (¹¹/₃₀₀)d(F - 13)

Where;

F is the strength of the steel in kilopound per square inch.

d is the diameter of the rocker in millimeters.

From the given formula, we can start by;

Multiply both sides by 300 to get;

300F = 11d(F - 13)

Divide both sides by 11(F - 13) to get;

d = 300F/(11(F - 13))

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Four student government officers want to go to the state convention. It will cost them $100 for registration, $375 for transportation and food, and $41 per person for the hotel. There is $425 budgeted for the convention in the student government savings account. They can earn the rest of the money they need by having a car wash. If they charge $5 per car, how many cars must they wash in order to have enough money to pay for the trip?

cars___?

Answers

Answer:

$100 + $375 + $41(4) = $516

$516 - $425 = $91

$91 / $5 = 18.2 cars

Therefore, the four student government officers must wash 18 cars in order to have enough money to pay for the trip.

Joshua's cousin pledged $12 for a charity walk if Joshua walked 3 miles how much did his cousin pay per mile

Answers

Answer: $4 per mile

Explanation: 12/3 = 4
Joshua’s cousin paid $4 per mile because $12/3 miles is $4 per mile

what is m=5 n=3 mn+9

Answers

Answer = 2

Since m = 5 and n = 3, mn means multiply the values together.
5(3) = 15

Now add 9
15 + 9 = 24

Answer: 24

Step-by-step explanation:

Given that m=5 and n=3, we can plug our values into the given expression to evaluate.

(5)(3)+9                  [multiply]

15+9                        [add]

24

The reason we multiplied before we added was due to the order of operations. Order of operations tells us to always multiply or divide first before we add or subtract. In this case, the multiplication happens to come first so we multiply, then add.

List the data in the following stem-and-leaf plot. The leaf represents the tenths digit.
Separate the numbers in the list by a comma. The list is:
151,154,154,157,165,166,178,183,186,186

Answers

The data represented by the steam-leaf plot is 115, 138, 145, 145, 156, 166, 168, 168, 175, and 187.

What is a stem leaf plot?

A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

A stem and leaf plot is shown as a customized table with the first or final digit of each data value divided into a stem and the remaining digit in a leaf.

9 I 0 ⇒ 9 on the stem and 0 on the leaf read as 90.

Given, A stem leaf plot and the leaf represents the tens digit.

As the leaf represents tens digits the data set can be represented by,

115, 145, 145, 175, 156, 166, 187, 138, 168, 168.

Representing the data set in ascending order we have,

115, 138, 145, 145, 156, 166, 168, 168, 175, 187.

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Please answer question 10 and 11 please

Answers

Answer:

d7-dx=(20x|x-3|+40)x  x-3 (|x-3+2)x| x-3|

Step-by-step explanation:

Hope this helps :D

prime numbers of the form p and p+2, where p is a prime number, are known as ______ prime numbers

Answers

Prime numbers of the form p and p+2, where p is a prime number, are known as twin prime numbers.

What is the Prime numbers about?

A twin prime is a prime number that is either 2 less or 2 more than another prime number. For example, the number 3 and 5 are twin primes, because they are both prime and the number 5 is 2 more than 3. Similarly, the number 5 and 7 are also twin primes, because they are both prime and the number 7 is 2 more than 5.

Therefore, Twin primes are considered as interesting numbers in number theory because of their relative rarity, rare in nature and because they are the building blocks for certain types of primes such as Sophie Germain primes and safe primes.

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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Write the quotient as a mixed number.
26÷3=8 R2

Answers

When we divide 26 by 3 we get 8 as a quotient and 2 as a remainder, the Mixed Fraction is [tex]8\frac{2}{3}[/tex]

What is a mixed Number ?

A full number plus a legal fraction are combined to form a mixed number. Mixed numbers, commonly referred to as mixed fractions, make it easier for humans to comprehend numbers.

A full number and a legal fraction make up a mixed number. A mixed number like [tex]2\frac{x}{y}[/tex] is one where 1/4 is the correct fraction and 2 is the whole number portion. It should be emphasized that once mixed numbers are transformed into an incorrect fraction, they are simple to add, subtract, multiply, and divide.

Steps to convert Improper fraction to Mixed Fraction :

Divide the numerator by the denominator to obtain the remainder and quotient as the first step. 43 divided by 9 in this situation yields 4 as the quotient and 7 as the remainder.Step 2: This quotient (4) becomes the mixed number's whole number component. While the denominator stays the same, the remainder (7) becomes the numerator portion.Step 3: As a result, 43/9 becomes a mixed number and is written as , meaning that 43/9 = [tex]4\frac{7}{9}[/tex].

So when we divide 26 by 3 we get 8 as a quotient and 2 as a remainder so the Mixed Fraction is : [tex]8\frac{2}{3}[/tex]

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In 1965, the population of a country was 192 thousand to 3 significant figures.

In 2020, the population of that country was 366 thousand to 3 significant figures.

Work out the percentage increase in population. Give your answer correct to 2 significant figures.

Answers

The percent change in population is 90.65%.

What is percent?

A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".

Given population of country in 1965 = 192 thousand = 1,92,000.

population of country in 2020 = 366 thousand = 3,66,000

the increase in population is = 366000 - 192000 = 1,74,000

the percentage increase =  (100)(increase in population)/(1965 population)

the percentage increase = (100) (174000)/(192000)

the percentage increase =  90.625%

Hence the percent increase is 90.62%.

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What is the vertex of the function?
f(x) = 3(r - 2)2 + 4

Answers

Answer:

(2,4)

Step-by-step explanation:

The vertex of a parabola in the form of [tex]y=a(x-h)^2+k[/tex] is [tex](h,k)[/tex]. In this function, we have [tex](2,4)[/tex] as our vertex.

How many rectangular faces are in a right triangular prism?

Answers

Answer: A right triangular prism is a 3-dimensional geometric shape that has a triangular base and three rectangular faces that connect the base to the top. A rectangular prism has three pairs of rectangular faces that are congruent, these faces are perpendicular to each other and connected by edges.

So, in a right triangular prism there are 3 rectangular faces which are the lateral faces (the one that connects the base and the top)

A triangular prism also has 3 triangular faces which are the base faces

So in total, a right triangular prism has 3 rectangular faces and 3 triangular faces.

Step-by-step explanation:

The density of a certain material is such that it weighs 6900 grams for every 4.5 quarts of volume. Express this density in pounds per cubic foot. Round your answer to the nearest whole number.

Answers

The density in terms of  pounds per cubic foot is 101.2 pounds/ft³

What is the unitary method?

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here; 6900 g for every 4.05 quarts thus expressing in terms of pounds per cubic foot we get = 15.22/0.15039

                                                  = 101.2

Hence, The density in terms of  pounds per cubic foot is 101.2 pounds/ft³

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Which of the following tables represents a linear relationship that is also proportional
Answer picture below ​

Answers

Answer:

c=200+0.4Yd find determine equlibirum level investment is =400

Answer:im pretty sure its D

Step-by-step explanation:it goes through the origin

Make equivalent fractions with the LCD of 12:

5/6 + 1/4 =


5/12 + 1/12 =


10/12 + 3/12 =


7/12 + 4/12 =


11/12 + 5/12 =

Which one?

Answers

Answer:

All four are equivalent fractions with the LCD of 12

Step-by-step explanation:

Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(0) = 2 B. g(-4) = -11 C. g(7) = -1 D. g(-13) = 20

Answers

A function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6 then g(-13) = 20

What is a function?

A relation is a function if it has only One y-value for each x-value.

Given a a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45

and that g(0) = -2 and g(-9) = 6,

x=-20 then g(-20)=-5

x=-19 then g(-19)=-4

x=-18 then g(-18)=-3

x=-17 then g(-17)=-2

x=-16 then g(-16)=-1

x=-15 then g(-15)=0

x=0 then g(0)=-2

x=-9 then g(-9)=6

By observing this we can say that as x values are decreasing the function values are increasing and vice versa

So option D is correct

Hence, a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6 then g(-13) = 20

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A satellite dish is in the shape of a parabolic surface. Signals coming from a satellite strike the surface for the dish and are reflected to the focus, where the receiver is located. The satellite dish has a diameter of 14 feet and a depth of 3 feet. How far from the base of the dish should the receiver be placed? Round your answer to the nearest tenth.

Answers

Answer:

Given that we know the base of the parabola is at the origin, and that it is symetrical about the y-axis, we can simplify the equation to

y=ax2=14px2" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">y=ax2=14px2y=ax2=14px2

which corresponds to the given equation a=14p" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">a=14pa=14p given above.

Since y=6" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">y=6y=6 when x=2" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">x=2x=2,

6=a(2)2=4a" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">6=a(2)2=4a6=a(2)2=4a

and

a=32" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">a=32a=32

Thus we have

32=14p12p=2p=16" role="presentation" style="display: table-cell !important; line-height: 0; text-indent: 0px; text-align: center; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 3.337em; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; width: 10000em; position: relative;">32=14p12p=2p=1632=14p12p=2p=16

So, the receiver should be placed 16" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">1616 of a foot, or 2 inches, above the base.

Which of the following sets of numbers could not represent the three sides of a triangles?



9,23,34
10,24,31
8,14,21
5,14,16


Answers

Answer:

pretty sure it's B. Let me know if im wrong

Step-by-step explanation:

Which radicals are already in the simplest form?

Answers

B E F
A can be broken down into 4 * 7
C can be broken down into 49 * 3
D can be broken down into 9 * 7

draw the graph of y=_3x_4​

Answers

Answer:

I can’t tell if both number are positive, ones negative ect but here’s the answer if both are negativ, let me know if the numbers are negative or positive and I can come back and give ya the right answer! Xoxo

Step-by-step explanation:

a ball is thrown from the top row of seats in a stadium the function h(t)=-16t^2+80t+96 gives the height, in feet, of the ball t seconds after it is thrown. how long will it be before the ball hits the ground?

Answers

The number of seconds it takes ball to before hit the ground is 6 seconds.

What is the solution of a quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

Given that, a ball is thrown from the top row of seats in a stadium the function h(t)=-16t²+80t+96 gives the height, in feet, of the ball t seconds after it is thrown.

When ball hits the ground h=0

So, -16t²+80t+96=0

-16(t²-5t-6)=0

t²-5t-6=0

By using splitting middle term method, we get

t²-6t+1t-6=0

t(t-6)+1(t-6)=0

t-6=0 or t+1=0

t=6 or t=-1

Time can not be negative integer.

Therefore, the number of seconds it takes ball to before hit the ground is 6 seconds.

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4 less than three sevenths as an algebraic expression

Answers

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operators.

To write "4 less than three sevenths" as an algebraic expression, we can use the variable x to represent the number we are trying to find, and then use subtraction and division to represent the parts of the phrase "4 less than three sevenths".

3/7x - 4 = an algebraic expression

or

x = 3/7y - 4

where x is the unknown value and y is any given value

Both expressions are algebraic representation of the statement "4 less than three sevenths"

XYZ Company
Balance Sheet
Assets
Cash
$45,000
Inventory $41,000
Property $134,000
Total Assets:
Liabilities
Notes
Wages
Equity
Stock
$55,000
$56,000
$50,000
Investment $59,000
Total Liabilities + Equity:
Using the balance
sheet, calculate XYZ
Company's total
assets - liabilities.
Total Assets - Liabilities = $ [?]
Enter
PH
Skip

Answers

On solving the provided question, we can say that - by formula of simple interest we have SI = [tex]2200 X 2 X 4/100 = > 17600/100 = > 176[/tex]

what is interest ?

Multiplying the principal by the interest rate, time, and other factors yields simple interest. Simple return equals principle times interest times hours is the marketed formula. It is easiest to compute interest using this formula. A percentage of the principle balance is how interest is most commonly computed. For instance, he will only pay his portion of the 100% interest if he borrows $100 from a buddy and promises to pay it back with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you lend money, you must charge interest. Most of the time, interest is expressed as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.

here

principal, p = 2200

rate, r = 2%

time, t = 4 rs,

so SI = P X R X T/100

SI -

[tex]2200 X 2 X 4/100\\17600/100\\176[/tex]

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Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°

Answers

Answer:

m∠5+m∠6=180°

m∠2+m∠3=m∠6

m∠2+m∠3+m∠5=180°

Step-by-step explanation:

Verify each option

case A) we have

m∠5+m∠3=m∠4 ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠5+m∠3=180°-m∠3

m∠5+m∠3+m∠3=180°

This equation is true when m∠2=m∠3

Therefore Is not always true

case B) we have

m∠3+m∠4+m∠5=180° ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠3+(180°-m∠3)+m∠5=180°

m∠5=0°

This option is not true

case C) we have

m∠5+m∠6=180°

we know that

m∠5 and +m∠6 are supplementary angles

so

Their sum is always 180 degrees

Therefore this option is always true

case D) we have

m∠2+m∠3=m∠6 -----> equation A

we know that

m∠5+m∠6=180° ----> by supplementary angles

m∠6=180°-m∠5 ----> equation B

substitute equation B in equation A

m∠2+m∠3=180°-m∠5

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

Therefore this option is always true

case E) we have

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

This option is always true

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