Griffen's house is 40 feet by 20 feet. He is building an attached deck that is x feet long and 13 as wide as it is long. Use the drop-down menus below to complete statements using words and symbols to describe the total area in square feet of the house and deck. CLEARCHECK Using Words The total area of the house and deck is given by the sum: + . Using Symbols The total area of the house and deck is given by the sum: ft² + ft².

A mall city had 5000 population of people in 2005 and 6200 in 2010, then the value of k is,

k = Log( [tex]\frac{\frac{Q(t)}{5000} }{t*log(e)}[/tex] )  ,  k = Log ( [tex]\frac{\frac{Q(t)}{6200} }{t*log(e)}[/tex] )

The value of t corresponds to the last two digits in the year.  

If t=0 represents the year 2000, then

For the year 2005,

t = 5

For the year 2010,

t = 10

First part of the problem.  

Find the value of k using these values.

Q(t) = 5000

t = 5

Q(t) = Qo[tex]e^{kt}[/tex]

Q(t) = 5000[tex]e^{kt}[/tex]

k is an exponential value.  When we solve for an exponential value, we must use logarithms.

First, divide both sides of equation by 5000

[tex]\frac{Q(t)}{5000}[/tex] = [tex]e^{kt}[/tex]

log both sides of the equation.

log(  [tex]\frac{Q(t)}{5000}[/tex] ) = log ([tex]e^{kt}[/tex] )

Next, bring the exponents down as the coefficients of the log.

log(  [tex]\frac{Q(t)}{5000}[/tex] ) = kt * log(e)

Divide by t*Log(e) both sides of equation to obtain k.

Log( [tex]\frac{\frac{Q(t)}{5000} }{t*log(e)}[/tex] )  = k

Now, plug in the values.

Second part of problem.  Find P using these values.

t = 10

Q(t) = Qo[tex]e^{kt}[/tex]

Q(t) = 6200[tex]e^{kt}[/tex]

k is an exponential value.  When we solve for an exponential value, we must use logarithms.

First, divide both sides of equation by 6200

[tex]\frac{Q(t)}{6200}[/tex] = [tex]e^{kt}[/tex]

log both sides of the equation.

log( [tex]\frac{Q(t)}{6200}[/tex] ) = log ([tex]e^{kt}[/tex] )

Next, bring the exponents down as the coefficients of the log.

log( [tex]\frac{Q(t)}{6200}[/tex] ) = kt * log(e)

Divide by t*Log(e) both sides of equation to obtain k.

Log ( [tex]\frac{\frac{Q(t)}{6200} }{t*log(e)}[/tex] ) = k

Now, plug in the values.

Therefore,

A mall city had 5000 population of people in 2005 and 6200 in 2010, then the value of k is,

k = Log( [tex]\frac{\frac{Q(t)}{5000} }{t*log(e)}[/tex] )  ,  k = Log ( [tex]\frac{\frac{Q(t)}{6200} }{t*log(e)}[/tex] )

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For the mathematical series, the total of the first 25 terms is 1850.

Arithmetic progression or arithmetic sequence is a numerical series in which the difference between subsequent terms is constant. For example, the sequence 5, 7, 9, 11, 13, 15.. An arithmetic sequence is a series of integers that are ordered and share a common difference between each succeeding term. In the arithmetic sequence 3, 9, 15, 21, 27, for example, the common difference is 6. An arithmetic progression is another name for an arithmetic sequence.

Here,

This is an arithmetic sequence as each term has a common difference to the previous term.  Any arithmetic sequence can be expressed as:

a(n)=a+d(n-1), a=initial term, d=common difference, n=term number.

We know that a=2 and d=(20-14)=(14-8)=(8-2)=6 so

a(25)=2+6(25-1)

a(25)=146  

The sum of an arithmetic sequence is the average of the first and last terms times the number of terms, in this case:

s(25)=25(2+146)/2

s(25)=1850

The sum of the first 25 terms is 1850 for the arithmetic sequence.

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Answer:

1. Convert to decimal notationThe exponent is -3, making it 10 to the power of negative 3. When an exponent is negative, the solution is a number less than the origin or base number. To find our answer, we move the decimal to the left 3 times: 4.0

 2. Final result

0.004

therefore Makayla runs = 3/5+3/5+3/5+3/5+3/5+3/5=18/5  = 3.6 miles in one hour

Makayla run 3/5 of a mile in 1/6 of an hour.

How far, in mile per hour, doe he run

in one hour = 1/6+1/6+1/6+1/6+1/6+1/6=1

therefore he runs = 3/5+3/5+3/5+3/5+3/5+3/5=18/5

 = 3.6

What is linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Driving separate vehicles on the same highway are Makayla and Addison,

another eample Makayla is 290 miles away from stadium,

Makayla driving speed is  40 miles per miles.

345 miles separate Addison from the stadium.

Addison driving speed is 51 miles per hour.

Let tt represent hours.

Therefore the equation is

Mm=290-40tt

Aa =345-51tt.

question

One​ month, two search engines were used to conduct a total of 3.52 billion online searches. Search engine A was used to conduct 0.66 billion more searches than search engine B. How many searches were conducted on each search​ engine?

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The resulting 3D shape would be a cylinder.

A cylinder is a geometrical shape which is three dimensional figure. It has two circular bases which are parallel and they are connected with a curves surface.

We have to find the resulting 3D shape when you repeated  the paper scaling with a piece of paper that was circular.

Suppose that we are scaling with a circular object like coin.

We place coins repeatedly on a surface where one coin is placed on the top of the last placed coin and then continue the process.

If you place coins on top of each other, it will result in a cylinder.

Hence the scaling of circular piece of paper repeatedly results in a cylinder.

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Answer: 14

Step-by-step explanation: Because if altogether they have 22 and Kevin already has 8 then you just add 14 more

This prompt is about being able to represent time and distance on a graph called Distance-Time Graph. See the graph attached.

A Distance-Time Graph is a sort of graph that depicts the relationship between distance and time for a moving object.

It is a handy tool for studying an object's motion since it allows one to simply ascertain the object's speed and acceleration. It is also significant because it gives a visual depiction of an object or subject's motion, making the underlying physical ideas easier to grasp.

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Full Question:

Tanisha left her house at time zero and drove to the store, which is 8 blocks away, at a speed of 4 blocks per minute. Then she stopped and went into the store for 3 minutes. From there, she drove in the same direction at a speed of 3 blocks per minute until she got to the bank, which is 12 blocks away from the store. She stopped at the bank for 7 minutes. Then she drove home at a speed of 5 blocks every 2 minutes. Make a graph of showing the number of blocks away from home that Tanisha is xx minutes after she leaves her house, until she gets back home.

Make a graph of showing the number of blocks away from home that Tanisha is x minutes after she leaves her house, until she gets back home.

The rate of flying explorer A is more than the rate of explorer B.

Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

here,
Proportionality equation for explorer A,
y=7000x
Rate of flying explore A = 7000

Rate of flying explore B,
Rate = distance / time = 84000 / 20 = 42000

Thus, the rate of flying explorer A is more than the rate of explorer B.

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Answer:

The Last Answer

Step-by-step explanation:

Process of elimination

He wants AT LEAST which means that is will be a less than symbol with a line under it, the last one is the only one with that!

a) Yes, the given triangle is Angle - Angle similarity posulate.

b) Yes , 2 triangles are similar using AA similarity posulate.

c) If the triangles are follow the AA similarity posulate then they are congruent to each other also.

What is triangle?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

What is AA similarity posulate?

According to the AA Similarity Postulate and Theorem, each triangle must have two matching angles that are congruent in order to demonstrate that two triangles are similar.

Think about the triangles which are given in the question;

ΔABC with scale factor of [tex]\frac{AB}{DE}[/tex]  to create ΔA'B'C'.

ΔABC is dilated about point P with a scale factor of [tex]\frac{AB}{DE}[/tex]  to create ΔA'B'C'.

After a dilation, corresponding angles are congruent, thus

∠B ≅ ∠B'

Therefore,  ∠B' ≅ ∠E.

Similarly, ∠A ≅ ∠A'

therefore, ∠A' ≅ ∠F . Due to the scaling factor being [tex]\frac{AB}{DE}[/tex]

A'B' = [tex]\frac{AB}{DE}[/tex] · AB = DE

So, [tex]\overline{A'B'}[/tex] ≅ [tex]\overline{F'E'}[/tex].

Now, we have to prove ΔABC [tex]\sim[/tex] ΔDEF.

We know that,

∠B' ≅ ∠E , ∠A' ≅ ∠F and [tex]\overline{A'B'}[/tex] ≅ [tex]\overline{F'E'}[/tex].

This means that,

ΔA'B'C' ≅ ΔDEF by ASA rule.

Consequently, a series of stiff transformations must occur that will convey;

ΔDEF to ΔA'B'C' then there will be a dilatation.

ΔA'B'C' to ΔABC.

About the initial two triangles, it was all that was known was two sets of parallel angles. You have therefore demonstrated that AA is a need for triangle similarity.

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Yes, the sides 7 cm 24 cm 25 cm form a right angled triangle.

The right angled triangle contains hypotenuse, which is opposite the 90° angle. Other two sides are base and perpendicular. The side of right angled triangle follows Pythagoras theorem.

It says, hypotenuse² = perpendicular² + base²

We know 25 cm will be hypotenuse as it is the longest side. Keeping the values now -

25² = 24² + 7²

Taking square of all the values

625 = 576 + 49

Performing addition on Right Hand Side of the equation

625 = 625

As the square of hypotenuse is equal to sum of square of other two sides, it is right angled triangle.

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If a set of data has a normal distribution with a mean of 50 and a standard deviation of 8. the percent of data within the interval less than 50 is; C. 50%.

Based on the details given the percent of data within the interval less than 50 is not 34% or 68% or 97.5% but rather the percent of data  is 50%.

The reason why it is 50% is that  the mean is 50 in which the data has a normal distribution, 50 is the center of the distribution.  Based on this half the data falls above the mean and half the data falls below the mean.

Therefore the correct option is C.

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We use Section formula for internal division: P(x, y) = x = (m₁x₂ + m₂x₁)/(m₁+ m₂) and y = (m₁y₂ + m₂y₁)/(m₁+ m₂).

Section formula for external division: P(x, y) = x = ((m₁x₂ - m₂x₁)/(m₁+ m₂) , y = (m₁y₂ - m₂y₁)/(m₁+ m₂).

What is the section formula?

In coordinate geometry, the Section formula is used to determine the internal or external ratio at which a line segment is divided by a point. It is used to determine a triangle's centroid, incenter, and excenter. It is employed in physics to identify equilibrium locations, system centers of mass, etc.

Here,

We have to find the use of the section formula.

we concluded that the section formula is used for internal division: P(x, y) = x = (m₁x₂ + m₂x₁)/(m₁+ m₂) and y = (m₁y₂ + m₂y₁)/(m₁+ m₂).

Section formula for external division: P(x, y) = x = ((m₁x₂ - m₂x₁)/(m₁+ m₂) , y = (m₁y₂ - m₂y₁)/(m₁+ m₂).

Hence, the section formula is x = (m₁x₂ + m₂x₁)/(m₁+ m₂) and y = (m₁y₂ + m₂y₁)/(m₁+ m₂).

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u have to use the inequity expresstion to anwser the perentieses first it would come out to be a persent then turn that to a fration by devieding by the first numer in the perenthies by sencond number the answer would be 3 over six but negitive

The cost of one bag of pretzel is $ 1.80

The cost of one bag of granola bars is $ 3.15

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the cost of one pretzel be represented as x

Let the cost of one granola bar be represented as y

Now , the equation will be

4 bags of pretzels and 2 boxes of granola bars for $13.50

Substituting the values in the equation , we get

4x + 2y = 13.50   be equation (1)

And , 1 bag of pretzels and 5 boxes of granola bars for $17.55

Substituting the values in the equation , we get

x + 5y = 17.55   be equation (2)

Multiply equation (2) by 4 , we get

4x + 20y = 70.2   be equation (3)

Subtracting equation (1) from equation (2) , we get

18y = 56.70

Divide by 18 on both sides of the equation , we get

y = $ 3.15

So , the cost of one granola bar is $ 3.15

Substituting the value of y in equation (1) , we get

4x + 2 ( 3.15 ) = 13.50

4x + 6.30 = 13.50

Subtracting 6.30 on both sides of the equation , we get

4x = 7.20

Divide by 4 on both sides of the equation , we get

x = $ 1.80

So , the cost of one pretzel is $ 1.80

Hence , the equations are solved

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The value of x that makes △PQR ∼ △TUV is 27.

What is the similarity of triangles?

The similarity of triangles refers to the relationship between two or more triangles in which the corresponding angles are congruent (equal in measure) and the corresponding side lengths are in proportion.

Two triangles are similar if and only if the corresponding angles are congruent and the corresponding side lengths are in proportion.

If △PQR ∼ △TUV, then we can write:

PQ/UV = QR/UT = RP/VT = k (the proportionality constant)

If we know the value of two of the sides in one triangle and the corresponding two sides in the other, we can find the value of k.

we know that,

PQ = 27, TU = 18, QR = 36, and UV = x.

We can find the value of k by using the proportionality constant:

k = PQ/UV = 27/x

Then we can use k to find the value of RP:

RP/VT  = k, so RP = k * VT

We can find the value of VT by using the similar triangles:

QR/UV = RP/VT,

QR/UV = k,       ............(RP/VT  = k)

so,

(36/18) = (27/x) * VT

VT = (2/1) * (x/27)

Finally, we can find the value of x by solving this equation:

1/x = (2/1) * (1/(27*VT))

1/x = 2/(27*VT)

1/x = (2/1) * (1/(27*((2/1) * (x/27))))

1/x = (2/1) * (1/(27*(2/1) * (x/27)

1/x = (2) * (1/(27*2) * (x/27)

1/x² = 1/729

x = 27

Hence, the value of x that makes △PQR ∼ △TUV is 27.

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The x - intercept and y - intercept of the linear function are 10 and 4

A graph of a linear function is a straight line. The line will always pass through the origin (0,0) and have a constant slope. The equation for a linear function is y = mx + c, where m is the slope of the line and c is the y-intercept.

In this problem, we can model the linear function into the slope-intercept form and the plot using a graphing calculator.

-2x - 5y = -20

-5y = -20 + 2x

5y = 20 - 2x

y = (20 - 2x) / 5

y = 4 - 2/5x

Plotting this on a graph using a graphing calculator

The y - intercept is at 4, and the x - intercept is at 10

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The area of triangle with the base 24 centimetres and height 15 centimetres is 180 cm².

The area of triangle is calculated by the formula -

Area of triangle = 1/2 × b × h, where b represents base of the triangle and h represents height of the triangle.

Keep the values in formula to find the area of triangle.

Area of triangle = 1/2 × 24 × 15

Performing division on Right Hand Side of the equation

Area of triangle = 12 × 15

Performing multiplication on Right Hand Side of the equation

Area of triangle = 180 cm²

Thus, the area of triangle is 180 cm².

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Answer: 4. No, not Similar

Step-by-step explanation:

<QSR = 62

because of vertical angles

we have 3 different angles and no sides

The amount of the apple pie that was left will be 3/4.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

From the information, Bert found 2 1/2 of an apple pie in the refrigerator. He shared 1 3/4 of the pie with his friends.

The amount of the apple pie that was left will be:

= 2 1/2 - 1 3/4

= 3/4

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Complete question

Bert found 2 1/2 of an apple pie in the refrigerator. He shared 1 3/4 of the pie with his friends. How much of the apple pie was left?

Using similar triangle theorem, the similarity statement will be "ΔGJL ≈ Δ HLK".

Similar triangles are two or more triangles that have the same shape but may be different sizes. They have the same angles and sides that are proportional to each other.

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides. This proves that the ratio of the area of two similar triangles is proportional to the squares of the corresponding sides of both the triangles.

In this problem, we can see that both triangles are similar and have the same angle.

The correct similarity statement will be "ΔGJL ≈ Δ HLK"

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A) Leaving home in a car and going to a store, shopping for a while, and then coming back home (the direction of the store is positive) figure 2.

B) Rolling a marble down the stairs (the bottom of the stairs is the origin)  figure 6.

C) Rolling a marble towards a table (the direction from which the marble came was the negative direction). figure 1.

The graphs are extremely helpful and widely used data structures. They are applied to a wide range of object relationships and, in reality, are applicable to almost everything.

The graphs represent a generalised structure that allows for the modelling of a very broad range of real-world situations, as we shall see in more detail. Trees are a subset of graphs, and lists are special cases of both trees and thus of graphs.

Since graphs are frequently used in practise, there has been a great deal of research into "graph theory," where there are many known problems for graphs and many well-known solutions to them.

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So on solving the provided question, we can say that Area of rectangle, A = 3x*x => x = 5

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

here, length is 3 times breadth

so let length = x

breadth = 3x

Area of rectangle, A = 3x*x

A = 3x^2

75 = 3x^2

x = 5

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Answer: If Shelly made 19 treat bags, and 11 of them were for girl guests, then the remaining bags were for boy guests.

So the number of boy guests = 19 - 11 = 8

Then the ratio of boy guests to girl guests is 8:11

or you can simplify it by dividing 8 and 11 by greatest common factor which is 8/11 in this case.

or you can express it as 8/19 for boy guests and 11/19 for girl guests

Step-by-step explanation:

Casey would pay the same amount to be a member of either gym in 6 months and that amount would be 360 dollars, that is $360.

Let the number of months be x.

In the 1st gym there is a $150 joining fee and cost $35 per month. So after x months the total cost in dollars in first gym is

= 150 + 35x

In the 2nd gym there is no joining fee and cost $60 per month. So after x months the total cost in dollars in second gym is

= 60x

When Casey pay the same amount to be a member of either gym, the total cost of the gym would be equal

150 + 35x = 60x

25x = 150

Dividing by 25

x = 6

The amount she pay to be a member of either gym when there is same amount is

= 60×6

= 360

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Therefore , the solution of the given problem of test statistics comes out to be in light of this, Z = 1.19 is the answer to the test statistic puzzle.

A test statistic in a research study is the figure that is applied to decide whether to confirm or refute hypothesis. This statistic compares the results of a study or sample to what the null hypothesis would predict.

A conjecture is a proposal that makes sense in light of the available information but has neither been confirmed nor refuted. A assertion on which hypotheses will be based is referred to as a hypothesis in statistics (also known as a statistical hypothesis).

Here,

given:

=> 60= μ

=> 15.9 = σ

=> n=40

=>x' = 63

utilized formula is

=> Z = (x' - μ) / σ/(√n)

=> Z = (63 -60) / 15.9 / √40

=> Z = 3 / 15.9/√40

=> Z = 3 / 2.5140

=> Z = 1.19

Therefore , the solution of the given problem of test statistics comes out to be in light of this, Z = 1.19 is the answer to the test statistic puzzle.

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Answer:

P(not red) = 90%

Step-by-step explanation:

There are 3 red, 3 green, 15 yellow, and 9 purple marbles in all:

3 + 3 + 15 + 9 = 30

You are trying to find the probability of not obtaining a red marble. There are 3 red marbles, and 30 marbles in all. This means that there are 27 marbles that are not red. Divide 27 with 30:

27/30 = 0.9

0.9 = 90/100 = 90%

90% is your answer.

P(not red) = 90%.

~

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Answer: 90%

Step-by-step explanation:

Answer:

6g+6h

Step-by-step explanation:

This is one way to re-write using the distributive property

Answer:

6g+6h

Step-by-step explanation:

The distributive property tells us how to solve expressions in the form of a(b + c). So, one simple way of rewriting the equation would just be 6g + 6h.