add -1[tex]\frac{1}{4}[/tex] 0.75 +0.45. Write your answer as a decimal to the nearest hundredth.

Answers

Answer 1

Answer:

Step-by-step explanation:

-0.05

Answer 2

Answer: -1/20, or -0.05

Step-by-step explanation:

rewrite -1 1/4 as -5/4

rewrite 0.75 as 75/100 and simplify = 3/4

rewrite 0.45 as 45/100 and simplify = 9/20

-5/4+3/4 = -2/4 = -1/2

-1/2+9/20 find LCD

LCD = 20

-1/2 * 10/10

-10/20+9/20= -1/20


Related Questions

If you chose the letters D and H for 20 turns, how many times are you most likely to win?

A. 1
B. 2
C. 3
D. 4
E. 5

edmentum

Answers

If you chose the letters D and H for 20 turns, the number of times you are most likely to win is; Option C: 3

What are the number of ways of winning?

We are given the probability of winning for each letter as;

A = 5%

B = 10%

C = 15%

D = 5%

E = 5%

F = 25%

G = 10%

H = 10%

I = 10%

J = 5%

Now, we want to find the number of times you can win If you chose the letters D and H for 20 turns.

Thus;

Number of times you can win if you chose Letter D = 5% * 20 = 1 time

Number of times you can win if you chose Letter H = 10% * 20 = 2 times

Thus;

Total number of ways of winning = 1 + 2 = 3 times

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What is the first step to solving the equation -2(3x + 8) - 2 = 10 ?
Combine like terms.
Distribute the -2.
Add 3x + 8.
None of these choices are correct.
Simplify: -3x + 6-3x-24 + 2y
-6x + 2y - 18
2y - 18
6x + 2y - 30
None of these choices are correct.
Solve: 5x = 13
8
18
13
51
65
Solve: 6r-17r=-66
6
-6
-11
11
Solve: P = 2/+ 2w for w
P-21
4/w
P-4/w
None of these choices are correct.
Solve: 4(9y-5) = 10(3y +17) - 40
20
25
-10
10

Chicago's high temperature for a given month is 88 degrees Fahrenheit and the low temperature is 65 degrees Fahrenheit. Which inequality represents the model?
3x+5<2x-8 is:
x2 65 or x ≤ 88.
65 ≤ x ≤ 88.
88 ≤ x ≤ 65.
None of these choices are correct.
V= /wh when solved for his:
all values more than -13.
all values less than -13.
all values less than 3.
all values less than -3.
h=
V
lw
h=V-lw
h = V + lw
h = Vlw

Answers

Answer:

x = [tex]\frac{-14}{3}[/tex]

Step-by-step explanation:

-2(3x + 8) -2 = 10  Distribute the -2

-6x - 16 -2 = 10 Combine like terms

-6x - 18 = 10   Add 18 to both sides

-6x = 28  Divide both sides by -6

x = [tex]\frac{-28}{6}[/tex] = [tex]\frac{-14}{3}[/tex]

7.Show that quadrilateral FGHJ is a trapezoid, but is not a parallelogram.

Answers

Answer:

FJ is -3/1

Step-by-step explanation:

And in order to be a trapezoid, just one pair of sides needs to be parallel.

(10x12) + (5x11) + (12x12) = Y

Answers

Answer:

Y= 319 hope you have the best rest of the day of your life ever. can i have brainliest

Step-by-step explanation:

Steps for Solving Linear Equation

(10×12)+(5×11)+(12×12)=Y

Multiply 10 and 12 to get 120. Multiply 5 and 11 to get 55. Multiply 12 and 12 to get 144.

120+55+144=Y

Add 120 and 55 to get 175.

175+144=Y

Add 175 and 144 to get 319.

319=Y

Swap sides so that all variable terms are on the left hand side.

Y=319

function rule to find f(10).

Answers

Answer:

[tex]f(10) = 103[/tex]

Step-by-step explanation:

f(x) = 3+10x

when x is 10, we have

3+10*10

= 103

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find the coordinates of the centroid of the triangle with the given vertices s(2,5) t(6,5) r(10,0)

Answers

Answer:

(6,[tex]\frac{10}{3}[/tex])

Step-by-step explanation:

[tex]\frac{2+6+10}{3}[/tex], [tex]\frac{5+5+0}{3}[/tex]

(6, [tex]\frac{10}{3}[/tex]) o r(6, 3 [tex]\frac{1}{3}[/tex])

The centroid of the triangle with the given vertices s(2, 5) t(6, 5) r(10, 0) is,

⇒ (6, 10/3)

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Three vertices of the triangle are,

⇒ s(2, 5) t(6, 5) r(10, 0)

Now, We can find;

The centroid of the triangle with the given vertices s(2, 5) t(6, 5) r(10, 0) is,

⇒ (2 + 6 + 10) / 3, (5 + 5 + 0) / 3

⇒ (6, 10/3)

Thus, The centroid of the triangle = (6, 10/3)

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The value of x when g(x) = 3

Answers

After solving the given equation at g(x) = 3 the value obtained is 3.

What is an equation?

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the information given in the question,

The given equation is,

g(x) = -2x + 9

Then,

g(3) = -2(3) + 9

= -6 + 9

g(3) = 3

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Your question seems incomplete, the complete question may be:

If g(x) = -2x + 9, what is the value of x

when g(x) = 3?

the discriminant of a quadratic function is 64 and its vertex is in quadrant III. Identify and explain 3 things you know about the function and /or its graph

Help PLEASE this due tommorow

Answers

Answer:

Step-by-step explanation:

If the discriminant of a quadratic function is 64 and its vertex is in quadrant III, here are three things you can know about the function and/or its graph:

The function has two distinct real roots. The discriminant of a quadratic function is the value under the square root in the quadratic formula:

x = (-b +/- √(b^2 - 4ac)) / 2a

If the discriminant is positive, it means that there are two real roots (values of x that make the equation equal to zero). If the discriminant is negative, it means that there are no real roots (the equation has no solutions). If the discriminant is zero, it means that there is only one real root (the equation has one solution). Therefore, if the discriminant is 64, it means that the function has two distinct real roots.

The graph of the function is a parabola that opens downward. The direction in which a parabola opens (upward or downward) is determined by the coefficient of the x^2 term (a). If a is positive, the parabola opens upward. If a is negative, the parabola opens downward. In this case, the vertex of the parabola is in quadrant III.

A 29.2-ounce bottle costs $5.37. what is the unit price?

Answers

The unit price is 0.183

Solve x for this diagram

Answers

Answer:

x = 20

Step-by-step explanation:

the 3 unknown angles form a right angle and sum to 90° , that is

x + 2x + x + 10 = 90

4x + 10 = 90 ( subtract 10 from both sides )

4x = 80 ( divide both sides by 4 )

x = 20

Answer:

x = 20°

Step-by-step explanation:

From the picture we know that x + 2x + x + 10 = 90°

x + 2x + x + 10 = 90

4x = 80

x = 80 : 4

x = 20°

--------------------

check

20 + 2 x 20 + 20 + 10 = 90

90 = 90

the answer is good

What is the order from least to greatest of the following: 0.8, −0.1, 1.1, and −1.5?

Answers

Answer:

I think -1.5 -0.1 0.8 1.1

Answer:

-1.5 || -0.1 || 0.8 || 1.1

Explanation:

Since it is from least to greatest, let's compare the 2 negative numbers -1.5 and -0.1.

-1.5 has a 1 in its first place while -0.1 has a 0. This means that -1.5 is smaller because the further a number is on the negative number line the smaller it is.

So, -1.5 is the smallest, then -0.1.

-1.5 || -0.1

Now we compare the 2 positive numbers 0.8 and 1.1.

0.8 has a 0 in its first place and 1.1 has a 1 in its first place. Because the numbers are positive, the number with the biggest digit in in front of the decimal is greater.

So, in this case 1.1 is greater than 0.8.

0.8 || 1.1

In order it is:

-1.5 || -0.1 || 0.8 || 1.1

The lengths of two sides of a triangle are 8 cm and 10 cm. Identify the range of possible lengths for the third side.

Answers

Given that the first two sides of a triangle are 8 cm and 10 cm in length, the third side's range of potential lengths will be [2,18].

What is range?

When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself. The difference between the highest and lowest values for a given data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3. As a result, the range can also be thought of as the distance between the highest and lowest observation.

Here,

The minimum length can be,

=10-8

=2 cm

The maximum length can be,

=10+8

=18 cm

(10-8)<x<(10+8)

2<x<18

The range of possible lengths for the third side will be [2,18] as The lengths of two sides of a triangle are 8 cm and 10 cm.

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4/6 x 3/5 in the simplest form.

Answers

Answer:

Step-by-step explanation:

2/5

parallelogram fghj was dilated and translated to form similar parallelogram f'g'h'j'. what is the scale factor of the dilation? 4 8

Answers

The scale factor of the dilation is s = 4 units .

Given :

parallelogram fghj was dilated and translated to form similar parallelogram f'g'h'j'.

To find scale factor between figures, find two corresponding sides and write the ratio of the two sides.

The value of y is same through the distance of F to G.

So, FG = change in x coordinates

FG = -2 - ( -4 )

= -2 + 4

= 2

F'G' = 3 - ( - 5 )

= 3 + 5

= 8

Let s be the scale factor

s = F'G' / FG

= 8 / 2

= 4

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What is the slope of this line?

Enter your answer as a whole number or a fraction in simplest form in the box.

Answers

Answer:

-1

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]

Define two points on the line:

Let (x₁, y₁) = (-2, 0)Let (x₂, y₂) = (0, -2)

Substitute the defined points into the slope formula:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-0}{0-(-2)}=\dfrac{-2}{2}=-1[/tex]

Therefore, the slope of the line is -1.

Is the system of equations consistent and independent, consistent and dependent, or inconsistent?

y=−x+1
2y=−2x+2



Select the correct answer from the drop-down menu.

Answers

After solving the equations it will the infinite solutions, then it is a consistent system.

What is an expression?

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.

A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given information in the question,

The equations are,

y = -x + 1  (i) and,

2y = -2x + 2  (ii)

Divide equation (ii) by 2

y = -x + 1 (iii)

Solve equation (i) and (iii)

The value of x and y will be 0 which means that it has infinite solution, then it is a consistent system.

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in the simplex method, the pivot column is the column with the most negative number (to the left of the vertical bar) in the bottom row. why?

Answers

The most negative number corresponds to the variable that has the largest impact on the Value of the objective function. So, maximizing it first is most efficient.

What is pivot column in simplex method?

The Simplex method's pivot column is selected by the fundamental variable's biggest reduced cost coefficient. 4. The highest ratio of right side parameters to positive coefficients in the pivot column determines the pivot row in the Simplex approach.

A location of a leading entry in the matrix's echelon structure. A pivot is a non-zero number that is either transformed into a leading 1 and then used to make 0s, or it is utilized in a pivot position to create 0s.

The element of a matrix or array chosen first by an algorithm (such as Gaussian elimination, simplex algorithm, etc.) to do particular computations is known as the pivot or pivot element.

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the sum of the ages of a father and his son is 38 years. if the father is 22 years older than his son , find their present ages ​

Answers

If the father is 22 years older than his son, and the sum of their ages is 38 years, we can set up the following equations to represent this information:

Copy code

father + son = 38

father = son + 22

We can solve for the father's and son's ages by substituting the second equation into the first equation:

Copy code

(son + 22) + son = 38

2 * son + 22 = 38

2 * son = 16

son = 8

Therefore, the son's age is 8 years, and the father's age is 8 + 22 = <<8+22=30>>30 years.

Answer:

16

Step-by-step explanation:

son=38-22

son=16

hope am correct

Find MK

Problem # 37
Please help!

Answers

Answer:

17.5

Step-by-step explanation:

Since the triangles are similar, the side lengths are proportional.  One way we can solve this is by finding the scale factor for the triangle on the left to the triangle on the right.  We can use the two corresponding sides that we know.

Let x = the scale factor

385x = 175  Divide both sides by 385

x = [tex]\frac{175}{385}[/tex]  Simplify by dividing the numerator and the denominator by 35

x = [tex]\frac{5}{11}[/tex]

Take the corresponding side of MK and multiply it by [tex]\frac{5}{11}[/tex] to find MK

38.5 x [tex]\frac{5}{11}[/tex] = 17.5

and his friends decided to have a water fight on a hot summer day. They filled a bunch of water balloons and started the fight at 1:00 P.M. The water balloons lasted for 1 hour. When all the water balloons were gone, they sprayed water with hoses for 30 minutes, until Rudy's dad showed up with ice cream. What time was it when the water fight ended?

Answers

Answer:

the water fight ended at 2:30pm

Step-by-step explanation:

the balloons lasted an hour bringing it to 2pm then they used the hoses for 30 min bringing it to 2:30pm

The width of a claroom i 4meter le than the length. It area i 45cm*45cm. Find the dimenion of the claroom

Answers

The dimensions of the classroom are a width is 5 m and a length is 9 m.

We have been given that the width of a classroom is 4m less than the length its area is 45m², then.

L= 4 + W

Area = 45, so

L x W = 45

Now substituting the value of L, we get.

(4+W) W=45,

Now simplifying this we get.

4W + W² =45

W² + 4W - 45 = 0, this is a quadratic equation

Now solving this we get the factors 9 and -5,

(W+9) and (W-5) = 0

Thus, W= -9 or W= 5, since the width cannot be negative,  

So, it is width = 5

So, length = 9 m

In physics and arithmetic, the dimension of a mathematical space (or item) is informally defined as the minimal range of coordinates to specify any factor within it. therefore, a line has a dimension of one (1D) due to the fact handiest one coordinate is wanted to specify a factor on it – for instance, the point at 5 on more than a few lines. A floor, together with the boundary of a cylinder or sphere, has a size of two (2d) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the floor of a sphere. A two-dimensional Euclidean area is a -dimensional area on the aircraft. The internal of a dice, a cylinder, or a sphere is 3-dimensional (3-d) due to the fact 3 coordinates are had to find a factor inside these spaces.

In classical mechanics, area and time are distinct classes and seek advice from absolute space and time. That theory of the sector is a four-dimensional space however not the only one that was discovered as essential to explain electromagnetism. The four dimensions (4D) of spacetime encompass activities that are not really described spatially and temporally, however as a substitute are acknowledged relative to the movement of an observer. Minkowski's area first approximates the universe without gravity; the pseudo-Riemannian manifolds of fashionable relativity describe spacetime with depend and gravity. 10 dimensions are used to describe the superstring principle (6D hyperspace + 4D), eleven dimensions can describe supergravity and M-principle (7D hyperspace + 4D), and the kingdom-space of quantum mechanics is an infinite-dimensional feature area.

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Step 1: we know that angle a b c is-congruent-to angle f g h because all right angles are congruent. step 2: we know that angle b a c is-congruent-to angle g f h because corresponding angles of parallel lines are congruent. step 3: we know that line segment b c is-congruent-to line segment g h because it is given. step 4: triangle a b c is-congruent-to triangle f g h because of the asa congruence theorem. aas congruence theorem. third angle theorem. reflexive property.

Answers

Based on the given steps the triangle ABC will be Congruent to triangle FGH because of the AAS Congruence .

What is AAS Congruence ?

the two triangle are said to be congruent based on the AAS Congruence when 2 angles and 1 non included side in one triangle are congruent to corresponding 2 angles and 1 non included side in another triangle.

So , in the question , based on the given steps we can say that ,
the two angles that are congruent is angle G and B , and angle A and angle F .

and the side that is congruent is BC = GH .

So  the triangle ABC and triangle FGH are congruent by AAS congruence .

Therefore , the correct option is (b) AAS Congruence Theorem .

The given question is incomplete , the complete question is

Step 1: we know that angle a b c is-congruent-to angle f g h because all right angles are congruent.

Step 2: we know that angle b a c is-congruent-to angle g f h because corresponding angles of parallel lines are congruent.

Step 3: we know that line segment b c is-congruent-to line segment g h because it is given.

Step 4: triangle a b c is-congruent-to triangle f g h because of the

(a) ASA congruence theorem.

(b) AAS congruence theorem.

(c) Third angle theorem.

(d) Reflexive property.

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18 2/6 Use the number line to round the mixed number to the nearest whole number.

Answers

Answer: The nearest whole number is 18

Step-by-step explanation: because 18 2/6 is closer to 18 than 19.

Kayden's math teacher said that each
question answered correctly on a test would
be worth 7 points. Answer the questions
below regarding the relationship between
the number of questions correct and the
score on the test.

Answers

Step-by-step explanation:

Kayden's math teacher said that each question answered correctly on a test would be worth 7 points. Answer the questions below regarding the relationship between the number of questions correct and the score on the test.

Since 00 questions correct gets you 00 points on the test, the function will have a yy-intercept of 0.0.

The rate at which points are earned is 7 points per question, so the slope of the function should be 7.7.

\text{Function Rule:}

Function Rule:

V(x)=7x

V(x)=7x

Plug x=11 Into Rule:

V(11)=7(11)=77

Correct Answer:

The independent variable, x, represents the number of questions correct, and the dependent variable is the score on the test, because the score on the test depends on the number of questions correct.

A function relating these variables is V(x) =V(x)= 7x7x.

So V(11) =V(11)= 7777, meaning 1111 questions correct will earn 7777 points on the test

what are three powers that have values greater than 120 and less than 130. ?

Answers

Answer: 11^2, 5^3, 2^7

Step-by-step explanation:

11^2= 121

5^3= 125

2^7= 128

Ue the ditributive property to rewrite the expreion a a multiple of a um of two number with no common factor. 24 18

Answers

36 is a multiple of two numbers added together without a common factor.

What is a common factor?

When a number is exactly divided by a divisor, that divisor is known as a factor of that number.

Alternatively, a factor of a number is an exact divisor of the provided number.

A number's factors are either less than or equal to the supplied number; they cannot be bigger. Every number is a factor of itself, and the common factor of all numbers is 1.

A number can be divided exactly by numerous divisors if it is a multiple of the divisor, therefore when we determine the factors of two or more numbers, we discover that some factors are common. As an illustration, the factors of 35 are 1, 5, 7, 35 while those of 45 are 1, 3, 5, 9, 15, 45. 1 and.

Hence, 36 is a multiple of two numbers added together without a common factor.

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Which ordered pairs is in the solution set of y>1/3 x+4

Answers

The ordered pair for the given solution set should be (-1, 6) when the graph solution set for the given inequality function is involved.

What is inequality function?

Since an inequality is merely a particular kind of relation, we can graph it just like we would any other relation. When dealing with inequalities, the trick is to shade large portions of the graph rather than using lines to connect the dots. But you could use some cover.

The given inequality function be like

y > 1 ÷ 3x + 4

The ordered pair refer to the solution set that provided by plotting the graph of the inequality, that expressed the inequality where an equation, plotting the graph along with a solid line, and shading the sides should be above the line of the graph to show the greater than or equal to sign.

Hence, the ordered pair for the given solution set should be (-1,6).

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I need help please!! Is 16% the correct answer?

Answers

Answer:

No, 16% is not the right answer.

It's:

Cars under 25 mph / Total Number of Cars

Cars under 25 mph:

I count 42 I think.

Total Number:

42 + 7 + 1 = 50

42 / 50 = .84

.84 * 100 = 84%

So, 84% of cars are moving below the speed limit.

A circular wheel makes 42 complete turns each minute.
How many degrees does it turn through in one second?

Answers

Answer:

252

Step-by-step explanation:

in each minute, the wheel makes 42 turns. That means it turns 42×360=15120 degrees in one minute (60 seconds). We want to find how many degrees it will turn in one second, not one minute, so we will divide the total degrees by 60.

15120÷60=252

So our answer is 252.

Two friends, Montraie and Serenity, took summer jobs. The equation y=19.2x represents Montraie's earnings in dollars and cents, y, for working x hours. Serenity earned $748.60 in 38 hours.


Use the dropdown menu and answer-blank below to form a true statement.


Montraie earns $___ per hour ___ (more or less) than Serenity.

Answers

Comparing the two friends earning Montraie earns $ 0.5 per hour less than Serenity

How to compare the earnings of the two friends

The word problem that has to do with earnings of two friends Montraie and Serenity is solved by putting the problem in equation form

The equations are generated as follows

The equation for the earning for Montraie is y = 19.2x

Using the equation in 38 hours Montraie will earn

y = 19.2 * 38

y = 729.6

This means that Montraie earns 19.2 per hour

For Serenity the earning per hour is solved

= 748.60 / 38

= 19.7

comparing both earnings

Serenity earning - Montaie earning

= 19.7 - 19.2

= 0.5

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Other Questions
at the division level, what integration cell is most likely responsible for conducting rdsp and issuing fragords based upon a change in the plan? Firms that operate in a market-directed economy attempt to develop ______ markets for themselves and their new products. Consider the relation belowIs it a function? Is the relation a one to one function? Is the inverse of the relation below itself of function ? hi can you please help me complete this work. Q3. Which of the following is the relation that the law of demand defines? a) Income and price of a commodity b) Price and quantity of a commodity c) Income and quantity demanded d) Quantity demanded and quantity supplied (7.8)(5) help me please Part of learning how to be a good writer is in learning to assess your own work and the work of others. So, in an effort to practice this skill, please choose one of your favorite works of fiction and evaluate how successfully the author was able to weave the theme through the story. Did the author utilize any of the following to weave in the theme: character actions, symbolic environment, repeating ideas, highlighting symbols, or contrasting values? Andy, Bobby, and Cindy each went for a walk yesterday afternoon. Andy walked 2 3/4 at a constant speed of 2 1/2 mi/h. Beth walked 1 3/4 mi at a constant speed of 1 1/4 mi/h. Cathy walked for 1 h and 16 min at a constant speed of 1 1/4 mi/h. List the three people in order of the times they spent walking from least time to greatest time. find the slope and y intercept for the graph of : 2x+4y=20 help plsAn observer moves to the left with some velocity, v, at the same time a sound wave source moves to the left with twice the velocity of the observer. How will the frequency of the source be shifted as it passes the observer?The observed frequency will be greater than the sources frequency.The observed frequency will be less than the sources frequency.The observed frequency will be the same as the sources frequency. The source never passes the observer. A firm must choose between two investment alternatives, each costing $100,000. The first alternative generates $40,000 a year for four years. The second pays one large lump sum of $161,200 at the end of the fourth year. If the firm can raise the required funds to make the investment at an annual cost of 10 percent, which alternative should be preferred? Which of the following statements is NOT a difference between movies and video games? A. Movies have been around for decades longer than video games. B. Movies show you the story, but video games allow you to shape the story. C. Video games have player agency, whereas movies usually do not allow viewers to make decisions that affect the plot. D. Movies always have a narrative, whereas video games usually do not. Can someone help me solve this inequality 5x = 7x +4 Given that ABCD is a rectangle, where EC=7 x-3 and AE=4 x+8 . Find DE. Which of the following is true regarding the relationship between a catalyst and a chemical reaction?Catalysts are not specific to reactions.A single catalyst can initiate many different types of reactions.Many catalysts are often involved in a single chemical reaction.Each reaction has its own unique catalyst. please help!!!! need help asap!!!!! The doctrine of caveat emptor means that the law may be justifiably used to restrict the freedom of individuals for their own good. A. TrueB. False The distribution of ages of licensed drivers shopping at the kalish county mall is normally distributed with mean 41 and standard deviation 7. A person will be selected at random. Round your answers to the nearest hundredth. The exclusionary rule was established to punish officers for their errors in collecting evidence by not allowing illegally obtained evidence to be admitted into a criminal hearing.TrueFalse A truck cost 60,000 it depreciate in value 4000 per year write a linear model in the form VT equals MT plus b