Amy simplified this complex fraction problem.

Negative 2 and one-half divided by five-fourths = Negative five-halves divided by five-fourths = negative five-halves (five-fourths) = negative StartFraction 10 over 8 EndFraction. The quotient is negative five-fourths.

What errors did Amy make? Select all that apply.

Step-by-step explanation:

A.Confidence Level: 99.7%; Confidence Interval: 42 to 48 

B.Confidence Level: 95%; Confidence Interval: 43 to 47

 C.Confidence Level: 68%; Confidence Interval: 44 to 46 

D.Confidence Level: 95%; Confidence Interval: 44 to 46

An expression for the number of tiles used by Bruce and Felicia are 5x + 2 and 5x + 5 respectively.

An expression refers to a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

Note: x represents the number of tiles in a box.

For Bruce, we have:

Expression = 3x + 2x + 2

Expression = 5x + 2.

For Felicia, we have:

Expression = 5x + 5.

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Complete Question:

Bruce retiled his kitchen. Originally, he bought three boxes of tile with the same number of tiles in each. He ran out of tile and had to go back to get three extra boxes of tile. However, he only used two tiles from the last box to finish the job.

Felicia also retiled her kitchen. She bought five boxes of tile, and each box contained the same number of tiles as each of Bruce’s boxes. She also ran out of tile. She had to go back to the store and get five more tiles to finish the job.

Write an expression for the number of tiles Bruce used and an expression for the number of tiles Felicia used. Use x to represent the number of tiles in a box.

Answer:

Bruce: y = 5x + 2

Felicia: y = 5x + 5

Answer:

0.00003mm

Step-by-step explanation:

We know that 1mm=1000000nm

To convert small unit to big we divide

So 30÷1000000=0.00003nm

[tex]\sqrt{(24-0)^{2}+(10-0)^{2}}=\boxed{26}[/tex]

Answer:

26

Step-by-step explanation:

√(24 - 0)2 + (10 - 0)2

= √(24)2 + (10)2

= √676 and that would equal

26

The true statement about the graph's slope is (c) Its slope is zero.

From the question, we have:

A horizontal line is at y = 2.5.

The horizontal line implies that the cost of lunch do not change

Horizontal lines have a slope of 0

Hence, the true statement about the graph's slope is (c) Its slope is zero.

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The value of this car when it is 9 years old is equal to $16,757.00.

In order to determine the value of this car when it is 9 years old, we would use an exponential function which also relates to compound interest as follows:

A = P(1 - r)^t

Substituting the given parameters into the formula, we have;

A = 32,200(1 - 0.07)^9

A = 32,200(0.93)^9

A = 32,200 × 0.5204

A = $16,757.00.

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The next step in constructing a line perpendicular to a point on the line is A. Place a compass at point D, and draw an arc that intersects the arc above line DF.

To make a perpendicular line:

Therefore, the next step would be to Place a compass at point D, and draw an arc that intersects the arc above line DF.

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The sample size which is required in order to estimate the mean per capita income at the 85% level of confidence with an error of at most $0.46 is 866.

Given mean income of $31.3 and standard  deviation of $9.4.

We have to calculate the  sample size of confidence interval of 85% and at an error of $0.46.

Margin of error is basically the difference between actual values and calculated values.

Mean =$31.3

Standard deviation=$9.4

Confidence level=85%

Margin of error=$0.46

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

0.46=1.44*9.4/[tex]\sqrt{n}[/tex]

[tex]\sqrt{n}[/tex]=1.44*9.4/0.46

[tex]\sqrt{n}[/tex]=29.42

squaring both sides

n=865.53

Round off and we get the following:

n=866.

Hence the sample size needed to estimate the mean per capita income at the 85% level of confidence is 866.

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Answer:

7 (option B)

Step-by-step explanation:

the area of a trapezoid can be found using the formula:

[tex]A = \frac{a+b}{2}h[/tex]

where

A: area

a: base

b: other base

h: height

here, we can plug in our known variables to solve for h (height)

A: 119

a: 10

b: 24

h: ??

[tex]A = \frac{a+b}{2}h[/tex]

[tex]119 = \frac{10+24}{2}h[/tex]

{now, simplify!}

[tex]119 = \frac{10+24}{2}h[/tex]         {add 10 + 24}

[tex]119 = \frac{34}{2}h[/tex]            {divide 34 by 2}

119 = 17 · h

119     =    17 · h

÷ 17       ÷17             {divide both sides by 17to isolate h}

7 = h

So, the height (h) of this trapezoid is 7

hope this helps! have a lovely day :)

Answer:

The expression for the statement using absolute value notation is [tex]$|p-0.08| \leq 0.015$[/tex].

Step-by-step explanation:

It is given in the question that the true proportion p of people who give a favourable rating to Congress is 8% with a margin of error of 1.5%. It is required to express the statement using absolute value notation.

To express the statement using absolute value notation, deduce the statement in the form of an equation.

The error margin for the hypothesis is 1.5% which implies the absolute difference between p and 8% should be less than or equal to 1.5%.[tex]$$|p-0.08| \leq 0.015$$[/tex]

Subtract the largest power of 2 from 798 such that the difference is not negative.

2⁹ = 512 and 2¹⁰ = 1024, so the largest power of 2 smaller than 798 is 2⁹, and

798 = 512 + 286 = 2⁹ + 286

Repeat this process with the remainder, 286.

2⁸ = 256, so

286 = 256 + 30 = 2⁸ + 30

⇒   798 = 2⁹ + 2⁸ + 30

2⁴ = 16 and 2⁵ = 32, so

30 = 16 + 14 = 2⁴ + 14

⇒   798 = 2⁹ + 2⁸ + 2⁴ + 14

2³ = 8, so

14 = 8 + 6 = 2³ + 6

⇒   798 = 2⁹ + 2⁸ + 2⁴ + 2³ + 6

2² = 4, so

6 = 4 + 2 = 2² + 2¹

⇒   798 = 2⁹ + 2⁸ + 2⁴ + 2³ + 2² + 2¹

or more completely,

798 = 1×2⁹ + 1×2⁸ + 0×2⁷ + 0×2⁶ + 0×2⁵ + 1×2⁴ + 1×2³ + 1×2² + 1×2¹ + 0×2⁰

Then the base-2 representation of 798 is

11 0001 1110₂

Work Shown:

f(x) = 5x - 7

f(3) = 5(3) - 7 .... every x replaced with 3

f(3) = 15 - 7

f(3) = 8

[tex] \: [/tex]

Given :

To Find :

Calculating the value of x :

[tex]\sf : \implies \: 5x - 7[/tex]

[tex]\sf : \implies \: 5(3) - 7[/tex]

[tex]\sf : \implies \: 15 - 7[/tex]

[tex]\bf : \implies \: 8[/tex]

Hence,

[tex] \implies \boxed{ \bf \: \therefore \: The \: value \: of \: x \: is \: 8 \: } \\ \\ [/tex]

Answer:

Step-by-step explanation:

There are several ways you can find the values of an exponential function for different values of the independent variable. You can read them from its graph, evaluate the formula, or recognize the relationship between the values.

The graph shows you the population is 10 in year 1, up by a factor of 2 from the population of 5 in year 0. The exponential nature of the function means the population will double in each of the next few years:

  2 years: 2 × 10 = 20

  3 years: 2 × 20 = 40

  4 years: 2 × 40 = 80

__

Additional comment

You can always use a calculator to evaluate the function for different values of t.

The change in volume is -88π

The volume is nothing but the amount of space occupied by a three-dimensional figure as measured in cubic units.

Volume Change is defined as the variation in the existing volume of the service type which is provided by the Supplier under the Agreement

The radius is decreasing at 2 inches per minute

The height is given as decreasing at 4 inches per minute

So let [tex]\frac{dr}{dt}=-2[/tex] and

[tex]\frac{dh}{dt}=-4[/tex]

and we have radius r=6,

                     height h=5

The volume of the cone is represented by V as V=[tex]\frac{1}{3}\pi r^{2}h[/tex]

Then

[tex]\frac{dv}{dt}=\frac{\pi }{3}[r^{2}\frac{dh}{dt} +h*2r\frac{dr}{dt}][/tex]

[tex]=\frac{\pi }{3}[6^{2}(-4)+5*2(6)(-2)][/tex]

[tex]=\frac{\pi }{3}[36(-4)+5(12)(-2)]\\ =\frac{\pi }{3}[-144+(-120)]\\ =\frac{-264}{3}\pi \\ =-88\pi[/tex]

So the volume change is [tex]-88\pi[/tex]

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By using the area formulae for triangles and rectangles and the concept of surface area of the composite figure is equal to 1108 square inches.

The surface area is the area of all faces of a solid. In this case, we must sum the areas of seven rectangular and two triangular faces to determine the surface area:

A = 2 · (0.5) · (12 in) · (9 in) + 2 · (11 in) · (20 in) + 2 · (5 in) · (20 in) + 2 · (5 in) · (12 in) + (12 in) · (20 in)

A = 1108 in²

By using the area formulae for triangles and rectangles and the concept of surface area of the composite figure is equal to 1108 square inches.

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Answer:

false

Step-by-step explanation:

these measure do not form a right triangle

Her work is correct, but there is one solution rather than no solution.

Linear equations are equations that has a degree of 1. Given the equation below;

3(2x + 1 ) = 2(x + 1) + 1

Expand

3(2x) + 3(1) = 2(x) + 2(1) + 1

Simplify

6x + 3 =2x + 2 + 2

6x + 3 = 2x + 3

Collect the like term

6x - 2x = 3 - 3

4x = 0

x =0

Hence we can conclude that Her work is correct, but there is one solution rather than no solution.

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A model without any simplifying assumptions b.is highly complex and likely unworkable.

As their call implies, simplifying assumptions are assumptions that are protected within the version to simplify the evaluation as tons as feasible. While a simplified version now does not predict the conduct of the actual issue within perfect bounds, too many simplifying assumptions have been made.

While a scientific version enables us to make predictions, it's more valued. As clinical models are representations of simplified explanations, they do not are looking for to explain each scenario or every detail. This means that medical models often aren't equal to the 'real international' from which they are derived.

Mathematical models can help college students apprehend and discover the that means of equations or valuable relationships.

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The index form of the expression is 5^-1m

Note that index form means in a power form

We have that;

= 4m/20m

Find the similar factor

= 1/5m

The inverse of a number, is that number to the power of -1

Then,

1/5m = 5^-1m

Thus, the index form of the expression is 5^-1m

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The angle that corresponds to ∠N after transformation is: A. ∠N'.

Transformation is a process of manipulating a figure to create an identical figure either by dilation, rotation, or translation.

In the transformation performed in the image shown below, the new image formed is congruent to the original figure. This means polygon LMNOP ≅ L'M'N'O'P.

Therefore, the angle that corresponds to angle N is: A. Angle N'

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Answer: A). Angle N'

Step-by-step explanation:

Hello !

[tex]\frac{25}{100}=0.25[/tex]

Have a nice day ;)

Answer:

25

Step-by-step explanation:

25

Answer: 25% of 100 is 25.

The two inequalities are:

a) y ≤ -2x + 5

b) y < 3x - 14

On the first graph, we can see that the shaded region is below the line and that the line is solid, so the inequality is of the form:

y ≤ line.

Now, remember that if the line passes through (x₁, y₁) and (x₂, y₂).

Then the slope is:

[tex]a = \frac{y_2 - y_1}{x_2 -x_1}[/tex]

We can see that the line passes through (2, 1) and (-1, 3)

Then the slope is:

[tex]a = \frac{1 - 3}{2 - 1} = -2[/tex]

So the line is:

y = -2*x + b

To find the value of b, we use the point (2, 1), then we get:

1 = -2*2 + b

1 = -4 + b

1 + 4 = b = 5

Then the first inequality is:

y ≤ -2x + 5

Now let's go to the other line equation, again the shaded region is below the line and this time the line is dashed, then:

y < line.

Two points on the line are (5, 1) and (4, -2)

Then the slope is:

[tex]a = \frac{1 - (-2)}{5 - 4} = 3[/tex]

y = 3*x + b

To find the value of b, we use the point (5, 1)

Then:

1 = 3*5 + b

1 = 15 + b

1 - 15 = b = -14

Then the inequality is:

y < 3x - 14

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The value of x such that f(x) = g(x) is x = 3

Given the following expressions as shown

f(x) = x^3-3x^2+2 and;

g(x) = x^2 -6x+11

Equate the expressions

x^3-3x^2+2 = x^2 -6x+11

Equate to zero

x^3-3x^2-x^2+2-11 = 0

x^3-3x^2-x^2 + 6x - 9 = 0

x^3-4x^2+6x-9 = 0

Factorize

On factorizing the value of x = 3

Hence the value of x such that f(x) = g(x) is x = 3

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The correct statements regarding the linear function are given as follows:

A linear function is modeled by:

y = mx + b

In which:

In this problem, the line goes through points (-6,-7) and (8,0), hence the slope is given by:

[tex]m = \frac{0 - (-7)}{8 - (-6)} = \frac{7}{14} = \frac{1}{2} = 0.5[/tex]

Hence:

y = 0.5x + b

When x = 8, y = 0, hence the y-intercept is given as follows:

0 = 0.5(8) + b

b = -4.

When x = -2, we have that:

y = 0.5(-2) - 4 = -1 - 4 = -5.

The points (–2, –5) and (8, 0) are also on the line.

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Answer:

B,C,E

Step-by-step explanation:

took the test on edge and got 100

Answer: False

Step-by-step explanation:

   This is not a function because the single input [x] of 6 has outputs [y] of 2 and 4, and the single input [x] of 12 has outputs [y] of 2 and 4.

   A function must have only one output [y-value] for every input [x-value].

Answer: no solution

Step-by-step explanation:

if we simplify this equation, we derive that 9=2.

this is a false statement, which means this equation has no real solutions.

Answer:

P = 60 inches

Step-by-step explanation:

Perimeter is the distance around the outside of a shape. So, to find perimeter, add up all the sides.

The side lengths were given, add them:

15 + 20 + 25

= 60

The perimeter is 60 inches.

The term that describes point N is centroid. The correct option is C. Centroid

The centroid of a triangle is the point in which the three medians of the triangle intersect.

The median is a line that joins the midpoint of a side and the opposite vertex of the triangle.

In the given diagram, we can observe that the lines join the midpoints of each side to the corresponding opposite vertex.

Point N is the point where the lines intersect.

Hence, the term that describes point N is centroid. The correct option is C. Centroid

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Answer:

B. Circumcenter

Have an Amazing day/night!!

The value of b in the expression is -2.

a + a + b = 14

b + b + c = 8

a + b + c = 18

Therefore,

2a + b = 14

2b + c = 8

c = 8 - 2b

Hence,

a + b + 8 - 2b = 18

a - b = 18 - 8

a - b = 10

2a + b = 14

a - b = 10

3a = 24

a = 8

8 - b = 10

b = 8 - 10

b = -2

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Answer:

a = 8

b = -2

c = 12

Step-by-step explanation:

a + a + b = 14

2a + b = 14 ⇒ ( 1 )

b + b + c = 8

2b + c = 8 ⇒ ( 2 )

a + b + c = 18 ⇒ ( 3 )

First, let us make a as the subject in equation 1.

2a + b = 14

2a = 14 - b

[tex]a=\frac{14-b}{2} \\a = 7-\frac{b}{2}[/tex]   ⇒ ( 4 )

Let us make c as the subject in equation 2.

2b + c = 8

c = 8 - 2b ⇒ ( 5 )

Now it is clear for us that, we can replace a & c with ( 7 - b / 2 ) & ( 8 - 2b ) respectively.        

And now let us solve the equation 3 to find the value of b.

[tex]a+b+c=18\\\\7-\frac{b}{2} +b+8-2b=18\\\\Combine\: \:like\:\: terms.\\\\[/tex]

[tex]15-\frac{b}{2} -b=18\\\\\frac{15*2}{1*2} -\frac{b}{2}-\frac{b*2}{1*2}=18\\\\\frac{30}{2} -\frac{b}{2}-\frac{2b}{2}=18\\\\\frac{30-3b}{2} =\frac{18}{1} \\\\Use\:\: cross\;\: multiplication[/tex]

[tex]30-3b=18*2\\\\30-3b=36\\\\30-36=3b\\\\-6=3b\\\\-2 = b[/tex]

And now let us find  the value of a

For that, let us use the equation 1. There, we can replace b with ( -2 ) to find the value of a.

[tex]2a+b=14\\\\2a-2=14\\\\2a = 14+2\\\\2a=16\\\\a=8[/tex]

Now, let us find the value of c.

For that, let us take the equation 2. There also, we can replace b with -2 to find the value of c.

[tex]2b+c=8\\\\2*-2+c=8\\\\-4+c=8\\\\c=8+4\\\\c=12[/tex]