t(n)=120+12n
solve the equation for t(n)=500

I agree with Andrea that Δ AEG ≅ Δ AFG by the AAS congruence postulate

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

The problem requires the prove by Angle - angle - Side = AAS to ensure that the the triangles are congruent

The AAS have it that the two triangles being compared should have their two angles and the side not included being equal

The Angle - Angle - Side = AAS, here include

< FA,G - < AFG - AG

< EAG - < AEG - AG

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Answer: Yes

Step-by-step explanation: Can this help , 81 ÷ 3 is 27 which is one of the factors in the 3 multiplications

56.78% of the penguins in the population have a weight between 13.0 kg and 16.5 kg, according to the usual distribution.

Given,

The mean of the population, μ = 15.1 kg

Standard deviation, σ = 2.2 kg

We have to find the percent of the penguins from the population have a weight between 13. 0 kg and 16. 5 kg;

Here,

z score = x - μ / σ

The ratio of the p-value of Z when X = 16.5 minus the p-value of Z when X = 13 indicates the percentage of penguins in the population whose weight is between 13.0 kg and 16.5 kg.

x = 16.5

z score = x - μ / σ

z = (16.5 - 15.1) / 2.2  = 0.64

Z = 0.64 has a p-value of 0.7389.

x = 13

z score = x - μ / σ

z = (13 - 15.1) / 2.2 = -0.95

Z = -0.95 has a p-value of 0.1711.

0.7389 - 0.1711 = 0.5678.

0.5678 = 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.

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Answer: 1.1

Step-by-step explanation:

10 * .11 is 1.1

When multiplying decimals by ten you move the decimal place once to the right.

Answer:

1.1

Step-by-step explanation:

0.11 x 10 = 1.1

You are moving the decimal point over once (x 10).

After Ann start to translate the document in 2 days, they need more 4.4 days to complete the work.

A unit work would take Ann 10 days to complete, means each day Ann completes 1/10 work

She works for 2 days, hence the work done = 2 x 1/20 = 2/10

The remaining work = 1 - 2/10 = 8/10

Then Ben joins.

A unit work would take Ben 12 days to complete, means each day Ben completes 1/12 work.

Each day, both Ann and Ben will complete:

1/10 + 1/12 = 11/60 unit work

The remaining work = 8/10

Hence, if each day 11/60 work can be completed, to complete 8/10 work, they need:

8/10 : 11/60 = 48/11 = 4.4 days

Therefore we can conclude, after Ann works for 2 days, they need more 4.4 days to complete the work.

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To solve for v, isolate the variable by dividing each side by factors that don't contain the variable.

Solve for v.

Hope this helps!

The matching numbers are:

1) 0.0000225 = 2 x 10⁻⁵

2) 219,000 = 2 x 10⁵

3) 3,40,000 = 3 x 10⁶

4) 297,000 = 3 x 10⁵

5) 0.0000034 = 3 x 10⁻⁶

What are Exponents?

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.

We have to match the following terms :

1) 0.0000225 = 2 x 10⁻⁵
we can write 0.0000225 as
2.25 / 100000
or, 2.25 / 10⁵
then, 2.25 x 10⁻⁵

2) 219,000 =  2 x 10⁵
as the numbers after 2 are 5
therefore we write 10⁵

3) 3,40,000 = 3 x 10⁶
as the numbers after 3 are 6
therefore we write 10⁶

4) 297,000 = 3 x 10⁵
we round off 297 as 300
as the numbers after 3 are 5
therefore we write 10⁵

5) 0.0000034 = 3 x 10⁻⁶
we can write 0.0000034 as
3.4/ 1000000
or, 3.4 / 10⁶
then, 3.4x 10⁻⁶

Hence, the matching numbers are:
1) 0.0000225 = 2 x 10⁻⁵
2) 219,000 = 2 x 10⁵
3) 3,40,000 = 3 x 10⁶
4) 297,000 = 3 x 10⁵
5) 0.0000034 = 3 x 10⁻⁶

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The value of  the function (f + g)(x) = [tex]x^{2}[/tex] -5x + 9

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

f(x) = - 2x + 4, g(x) = [tex]x^{2}[/tex] -3x + 5

(f+g)(x) = f(x) + g(x)

So by adding the two functions

(f + g)(x) = -2x + 4 + [tex]x^{2}[/tex] -3x + 5

(f + g)(x)  = [tex]x^{2}[/tex] -5x + 9

In conclusion, the value of [tex]x^{2}[/tex] -5x + 9

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{5}{7}}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so for the parallel line we're really lookikng for the equation of aline whose slope is 5/7 and that it passes through (-5 , 6)

[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ \cfrac{5}{7}}(x-\stackrel{x_1}{(-5)}) \implies y -6= \cfrac{5}{7} (x +5) \\\\\\ y-6=\cfrac{5}{7}x+\cfrac{25}{7}\implies y=\cfrac{5}{7}x+\cfrac{25}{7}+6\implies {\Large \begin{array}{llll} y=\cfrac{5}{7}x+\cfrac{67}{7} \end{array}}[/tex]

now, keeping in mind that perpendicular lines have negative reciprocal slopes

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{5}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{5}}}[/tex]

so for the perpendicular line we're really looking for the equation of a line whose slope is -7/5 and that it passes through (-5 , 6)

[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{7}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{7}{5}}(x-\stackrel{x_1}{(-5)}) \implies y -6= -\cfrac{7}{5} (x +5) \\\\\\ y-6=-\cfrac{7}{5}x-7\implies {\Large \begin{array}{llll} y=-\cfrac{7}{5}x-1 \end{array}}[/tex]

Answer:

Step-by-step explanation:

F 3/8x 3/8y

P(AIB) can be read as "the probability that A occurs given that B has occured. This is true.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.

Conditional probability is a measure of the likelihood of an event occurring given that another event has already occurred in probability theory.

Conditional probability: p(A|B) is the likelihood of event A occurring if event B occurs. For example, if you drew a red card, what is the likelihood that it is a four (p(four|red))=2/26=1/13? So there are two fours out of the 26 red cards (given a red card), so 2/26=1/13.

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Answer:

7, 7/1

Step-by-step explanation:

The ratio 7:49 can be simplified to 1:7.

Working together, they can mow the yard in 48 minutes.

Given data;

A lawn can be mowed by Wilma in 120 minutes. In 80 minutes, Vanessa can cut the same lawn. When working together, how long does it take Wilma and Vanessa to mow the lawn?

Let 't' is their time in minutes working together.

Add their rates of working to get their rate working together,

Wilma's rate: [ 1 lawn ] / [ 120 min ]

Vanessa's rate: [ 1 lawn ] / [ 80 min ]

Rate working together: [ 1 lawn ] / [ t min ]

1/120 + 1/80 = 1/t

Multiply both sides by 240t;

2t + 3t = 240

5t = 240

t = 48

It takes them 48 min to mow the lawn working together.

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1 task will complete in 12.5 minutes

The robot can complete 9.6 task in 1 hour

Given,

Number of task a robot can complete = 4

Time taken by robot = 5/6 of 1 hour

5/6 of 1 hour = 5/6 × 60 minutes

= 300/6

= 50 minutes

Then,

4 task takes 50 minutes

1 task = 50 minutes / 4 task

= 12.5 minutes

So,

1 task = 12.5 minutes

x task = 60 minutes

1 : 12.5 = x : 60

1/12.5 = x / 60

1*60 = 12.5*x

60 = 12.5x

x = 60/12.5 = 4.8

x= 4.8

Therefore,

The robot can complete 4.8 task in 1 hour

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Answer:

25

Step-by-step explanation:

6.3= 1 blanket

to find 4 blankets you multiply 6.3 by 4

6.3x4=25.2

to the nearest whole number

25

From the given triangle, the order of the sides DEF from shortest to longest is DE, DF, and EF.

Triangle:

The polygon with three edges known as sides and three vertices are known as triangle.

Given,

Here we have the triangle with their corresponding angle.

Now, we have to order the sides from shortest to longest.

Here in the given triangle we know the angles of m∠D = 61, m∠E = 60, and m∠F = 59.

By knowing this measures we can order the sides from shortest to longest, because angles are the opening between to sides, which means if the angle is wide, its opposite side that is in front of the angle is wide too, if the angle is narrow, its opposite side will be narrow.

In this case, the opposite side of ∠D will be the longest, because it is the largest angle. And the opposite side of m∠E will be the second longest, and finally the opposite side of ∠F will be the smallest.

From values, the shortest to longest the order is written as DE, DF and EF.

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The power of a test is measured by its capability of rejecting a null hypothesis that is false, so option C is the correct answer

what is power with respect to probability?

Power is defined as the probability of correctly rejecting the false null hypothesis. It is the measure of the capability of rejecting a null hypothesis that is false.

Power = P[ rejecting a null hypothesis that is false.]

So, option C is correct, the power of a test is measured by its capability of rejecting a null hypothesis that is false

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The system of equations represents their transportation costs is:

50 − 2. 5x = y

40 − 2x = y

The correct option is  (A)

Given,

In the question:

Kaisorn deposits $50. 00 onto her public transportation card.

It costs her $2. 50 per trip to ride the subway.

Thom deposits $40. 00 on his public transportation card.

It costs him $2. 00 per trip to ride the subway.

Now, According to the question:

x → represents  the number of trips

y → represents the amount remaining in each account

According to the given condition:

The system of equations represents their transportation costs is :

50 − 2. 5x = y

40 − 2x = y

Hence, The system of equations represents their transportation costs is:

50 − 2. 5x = y

40 − 2x = y

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If (x, y) represents the location of any point on the original square, the ordered pair which represents the coordinates of the corresponding point on the resulting square is: (0.4x, 0.4y).

In Geometry, dilation simply refers to a type of transformation which changes the size of a geometric object and the location of its points based on the scale factor, but not its shape.

In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects (shapes) such as equilateral triangles, square, quadrilaterals, polygons, etc., which can be used to either enlarge or reduce their size.

Generally speaking, the transformation rule for the dilation of a geometric object (square) based on a specific scale factor is given by this mathematical expression:

(x, y)      →    (SFx, SFy)  = (0.4x, 0.4y)

Where:

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Complete Question:

A square with the perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation.

If (x, y) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square?

answer choices

(0.4x, 0.4y)

(x + 20, y + 20)

(x + 0.4, y + 0.4)

(20x, 20y)

Answer:

565/0.666=848.348

Step-by-step explanation:

if you needed variables added to the equation then show a picture and I can answer it.

Answer:

Step-by-step explanation:

B

Answer 0,4

Answer:

(-5,-1)

Step-by-step explanation:

Start at the orginal.  This is (0,0), the middle of the graph.  From that point you move 5 spaces left.  That is the -5 in the answer.  Then from that point, you move one space down.  That is the -1 in the answer.

Answer:

Point form:

(18/11 , -8/11)

Equation form:

x=18/11 , y=-18/11

Answer:

a) ln(Length), ln(Time)

c)log(Length), log(Time)

e)Length, Time²

Step-by-step explanation:

Answer:

the person above me is correct!

Step-by-step explanation:

Answer:

2 : 5 or 2/5

Step-by-step explanation:

The ratio is 40 : 100, which can simplify into 2 : 5.

A shaded region above a solid boundary line matches the graph of the inequality y <|x-2| + 1.

What is inequality?

Inequality is a relationship between two expressions or values that is not equal to each other.

This inequality may be written in two ways:

(a) y < x - 2 + 1

   or

   y < x - 1

(b) y < -x +2 + 1

   or

    y < -x + 3

A graph of the inequality is shown below. The shaded region satisfies the inequality.

Hence, a shaded region above a solid boundary line matches the graph of the inequality y <|x-2| + 1.

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The set of ordered pairs that represent dilation factor of 2 is

a. A' (2, 12) B' (12, 12) C' (2, 4)

Dilation is a method of transformation which uses a scale factor. The scale factor determines if the dilation is magnification or shrinking

|0 < r < 1| is shrinking

|r > 1| is magnification

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

From the graph the coordinates are read and following the given transformation rule we have

preimage                           image

A (1, 6)   → (1 * 2, 6 * 2) →   A' (2, 12)

B (6, 6)  → (6 * 2, 6 * 2) →    B' (12, 12)  

C (1, 2)  → (1 * 2, 2 * 2) →    C' (2, 4)

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