Question 1(Multiple Choice Worth 2 points)
(Scale Factor MC)

A toy company is building dollhouse furniture. A rectangular door of a dollhouse has a height of 7 centimeters and a width of 3 centimeters. What is the perimeter of the door on a scale drawing that uses the scale 3:5?

33 cm
20 cm
14 cm
12 cm
Question 2(Multiple Choice Worth 2 points)
(Scale Factor MC)

A picture is 7 inches wide and 9 inches long. A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long. What scale factor was used to enlarge the picture?

9 over 7
7 over 9
31.5 over 7
7 over 31.5
Question 3(Multiple Choice Worth 2 points)
(Scale Factor LC)

Figure 1 and figure 2 are right triangles.

two right triangles labeled figure 1 and figure 2, where the legs of figure 1 are 3 units long and the legs of figure 2 are 4 units long

What scale factor was used to produce Figure 2 from Figure 1?

3
4
3 over 4
4 over 3
Question 4(Multiple Choice Worth 2 points)
(Scale Factor MC)

A triangle with a perimeter of 24 meters was created from a triangle with a perimeter of 3 meters using a scale factor. What is the scale factor?

8:1
28:1
32:1
72:1
Question 5(Multiple Choice Worth 2 points)
(Scale Factor MC)

A rectangular flag is 80 centimeters by 92 centimeters. What are the dimensions of a scale drawing of the flag using the scale 1:4?

20 cm by 23 cm
320 cm by 360 cm
8 cm by 9.2 cm
1.15 cm by 4.35 cm
Question 6 (Essay Worth 4 points)
(Scale Factor HC)

A rectangular oil painting is 14 inches wide and 24 inches long. A museum wants to create a larger print of the painting using a scale factor of 3.

Part A: What are the dimensions of the print, in feet? Show every step of your work. (2 points)

Part B: What is the area of the print, in square feet? Show every step of your work. (2 points)

The expression that represents that number of items collected by Team A is a=2b+4.

Given that in a hunt, two teams collected a number of items for their teams. Now the items collected by team A is 4 more than the twice of the items collected by the team B. Let the items collected by team A be 'a' and the items collected by team B will be 'b'.

Now, team A collected items are 4 more than the doubled value of team B.

The expression that represents the items collected by the second team, that is Team A is:

a=2b+4

Therefore the expression that represents items collected by team A is a=2b+4.

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the sum of each infinite geometric series sum is 36

If the ratio between any two consecutive terms in a series of numbers is always the same, the progression is said to be geometric. The ratio of any two successive terms in the sequence (common difference) must be the same for the sequence 2, 4, 8, or 16 to be a general prime.

S = a/1-r is a general formula for calculating the sum of an infinite geometric series, where s stands for the sum, a1 is the series first term, and r is the common ratio.

a = first term = 18

r = common ratio = 1/2

sum of Geometric progression

r< 1

S∞ = a/(1-r)

S∞ = 18/(1-1/2) =36

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The solution to this system of equations is (10, 50).

A graph of this system of equations is shown in the image attached below.

Based on the information provided above, one of the plan includes a membership fee of $10 and charges $4 for every DVD borrowed. Therefore, the total cost, y, can be represented by this equation:

y = 4x + 10    .......equation 1.

where:

x represents the number of DVDs borrowed in a month.

For the second plan, it costs $50 per month for unlimited DVD rentals. Therefore, the total cost, y, can be represented by this equation:

y = 50    ....equation 1.

By equating equation 1 and equation 2, we have the following:

4x + 10 = 50

4x = 50 - 10

4x = 40

x = 40/4

x = 10 DVDs.

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Answer:  NIKES

Step-by-step explanation:

BEFAUSE 5/2 IS THE WHG0LE D[IWJAEOIDHNC;SHCOWIADHJA[OISHWNIOD

Answer: the answer is nike

Step-by-step explanation: Because the shipping fee on callaway is more than the order.

We can estimate that there is about 1000 joules of kinetic energy in an average size helium balloon.

The amount of kinetic energy in an average size helium balloon can be estimated using the ideal gas law and the equipartition theorem.

Assuming the balloon is filled with helium at room temperature (around 298 K) and atmospheric pressure (around 1 atm), the volume of the balloon can be estimated to be around 0.5 m^3. The number of helium atoms in the balloon can be estimated using Avogadro's number, which is around 6.02 x 10^23.

Using the equipartition theorem, we can estimate the average kinetic energy of each helium atom in the balloon. At room temperature, each atom has an average kinetic energy of (3/2)kT, where k is the Boltzmann constant (1.38 x 10^-23 J/K).

Therefore, the total kinetic energy of the helium atoms in the balloon can be estimated as:

KE = (3/2)kT * N

where N is the number of helium atoms in the balloon.

Plugging in the estimated values, we get:

KE = (3/2) * (1.38 x 10^-23 J/K) * 298 K * 6.02 x 10^23

KE ≈ 9.95 x 10^2 J

Therefore, An average-sized helium balloon contains roughly 1000 joules of kinetic energy, according to our estimation. It's important to note that this is just an estimate, and the actual amount of kinetic energy in a helium balloon can vary depending on a number of factors such as the temperature, pressure, and size of the balloon.

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When factoring a tricky trinomial with a leading coefficient greater than 1, and you have more than one pair of factors for a term, it is usually best to try the pair of factors that multiplies to give the constant term first.

This is because when factoring a trinomial with a leading coefficient greater than 1, the first term will always have fewer factors than the last term, and it can be easier to find the correct pair of factors for the constant term than for the first term.

If the correct pair of factors for the constant term is found first, it can be easier to use that information to deduce the correct pair of factors for the first term.

In addition, once you have found one pair of factors for the trinomial, you can use the factoring by grouping technique to factor the trinomial completely. This involves grouping the terms of the trinomial in pairs, factoring out the greatest common factor of each pair, and then factoring out the greatest common factor of the resulting expressions.

Overall, when factoring a tricky trinomial with a leading coefficient greater than 1, it can be helpful to start by trying the pair of factors that multiplies to give the constant term first, and then using the factoring by grouping technique to factor the trinomial completely.

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The explicit formula and recursive formula of the geometric sequence is  Aₙ = 12(R)ⁿ⁻¹ where n is an integer.

It is given that in a geometric sequence, the second term and the common ratio are 6 and /2 respectively.

Now, we have to write the standard formula that can be further formulated as the explicit formula and recursive formula of the geometric sequence, The formula goes as,

Aₙ = A₁(R)ⁿ⁻¹

Here,

Aₙ is the nth term of the sequence. So, if we want the first term then will put n = 1, n= 2 for second term and so on.

Now, putting n = 2,

A₂ = A₁(R)²⁻¹

A₂ = A₁(R)

6 = A₁(1/2)

A₁ = 12

So, the explicit and recursive formula will be Aₙ = 12(R)ⁿ⁻¹.

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Answer:

y=-2 over 1x+18

Step-by-step explanation:

The graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

f(x) = x(x + 5)(x - 2)

x(x + 5)(x - 2) = 0

x = 0, x + 5 = 0, x - 2 = 0

x = 0, -5 and 2

The graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2

Hence, the graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2

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The distance from the town to the North Pole is approximately 2290 miles.

To find the distance in miles from the town to the North Pole, we need to calculate the length of the meridian arc from the town to the North Pole. The meridian arc is a portion of a great circle passing through the town and the North Pole.

The length of the meridian arc can be calculated using the formula:

Length = (π/180) x radius of the Earth x angle in degrees

where π is approximately 3.14159, and the radius of the Earth is 3960 miles.

Since the town is located at latitude 32°N, the angle between the town and the North Pole is 90° - 32° = 58°.

Plugging in these values into the formula, we get:

Length = (π/180) x 3960 miles x 58°

Length = (3.14159/180) x 3960 miles x 58

Length ≈ 2290 miles

Therefore, the distance from the town to the North Pole is approximately 2290 miles.

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If the gross income per month is $4000 , then the monthly disposable income will be $2920   .

To find the monthly disposable income, we subtract the various taxes from the gross income.

The Federal tax is = 10% of $4000 = $400  ;

The State tax is = 7% of $4000 = $280  ;

The City tax is = 3% of $4000 = $120  ;

and the Social security tax is = 7% of $4000 = $280  ;

So , the Total monthly tax is = $400 + $280 + $120 + $280 = $1080  ;

We know that the Monthly disposable income = Gross income - Total tax ;

⇒ Monthly disposable income = $4000 - $1080  ;

⇒ Monthly disposable income = $2920  .

Therefore, the monthly disposable income after taxes is $2920.

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answer:

if you multiply the 2 sides of the ratio by a number it will give you an equivalent ratio

5:8 = 10:16 multiplying by 2

5:8 = 15:24 multiplying by 3

5:8 = 20:32 multiplying by 4

5:8 = 25:40 multiplying by 5

5:8 = 30:48 multiplying by 6

5:8 = 35:56 multiplying by 7

and so on ...

The solution is, Option A. Line X

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

We have to identify the line which represents the function f(x) = 3x - 5

The given equation is y = 3x -5, in which slope of the line should be 3 and y- intercept is -5.

In these lines line x is having y-intercept as -5.

Line x passes through (1, 2) and (0, -5)

So slope of the given line will be = y2 - y1/ x2 - x1

= -5-2/ 0-1

= 3

Therefore, option A : Line X is the answer.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: (3 {m}^{5} )(4m {}^{9} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: (3 \times 4)(m {}^{5} \times m {}^{9} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: 12m {}^{(5 + 9)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 12m {}^{14} [/tex]

So, The correct choice is B.) 12 m¹⁴

The equation in standard form is x - 9y = -45.

The equation of a line in standard form is Ax + By = C, where x and y are variables and A, B and C are integers.

Given equation is y = 1/9 x + 5.

Here 1/9 is not an integer.

So multiplying the equation throughout by 9, we get,

9y = x + (5 × 9)

9y = x + 45

Subtracting both sides by x,

9y - x = 45

-x + 9y = 45

Multiplying throughout by -1,

x - 9y = -45, which is in standard form.

Hence the equation is x - 9y = -45 in standard form.

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The number of ways a dinner patron can select appetizers and vegetables will depend on the number of options available for each course.

Let's say there are "m" appetizer options and "n" vegetable options on the menu.

Then, the patron has m options for the appetizer course and n options for the vegetable course. To find the total number of ways the patron can select both courses, you would multiply the number of options for each course:

m x n ways

So, if the patron has 4 options for appetizers and 3 options for vegetables, the total number of ways the patron can select both courses would be 4 x 3 = 12.

Therefore, the number of ways a dinner patron can select appetizers and vegetables will depend on the specific number of options available for each course.

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Answer:

x = 4 twice.

Step-by-step explanation:

x^2-8x+ 16=0

Bring the constant to the other side.

x^2-8x=-16

Half the coefficient of x and square the result. Add to both sides.

x^2-8x+[-8/2]^2=-16+(-8/2)^2

x^2-8x+16= 16-16

x^2-8x+16=0

Now, whenever there's a perfect square constant, take the root of that constant. Since the coeff. of x is negative (-8),

(x-4)(x-4)=0  [-4^2=16 and -4+(-4)=-8]

Therefore, x-4=0 twice.

x=4 twice.

Hope this helps!  :]

Answer:

Y < (1/3) x - 5

The chance of a series of draws can be calculated while drawing from a collection of things (for instance, a deck of cards) without replacing the items after they are drawn.

Calculate the likelihood of the initial draw while accounting for the sample space's abundance of favourable outcomes. The probability of drawing two consecutive red marbles is 4/25.

Probabilities are always in the 0 to 1 range. Probability = Number of favourable outcomes / Total number of outcomes is the general formula for probability. Or. P(A) = f / N.

On the initial draw, there is a 2/5 chance of getting a red marble.

Out of the five marbles, there are two red ones.

On the second draw, there is still a 2/5 chance of drawing a red marble.

Probability of drawing a red marble on the first draw equals the probability of drawing two red marbles (Probability of drawing a red marble on the second draw)

= (2/5) × (2/5)

= 4/25

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The value of x the width of the solar panel is 18.5.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have Pythagoras theorem:

|AC|^2 = |AB|^2 + |BC|^2    

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

We are given that;

Length of base of panel= 40feet

Other length = 12feet

Now,

Applying the pythagoras theorum;

|AC|^2 = |AB|^2 + |BC|^2  

|AC|^2= 12^2 + 14^2

|AC|^2= 144+196

AC= 18.5

Therefore, by Pythagoras theorem x will be equal to 18.5.

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Answer: As the ratio of newts and toads, 3:4

Step-by-step explanation:

The mortgage loan amount on a home that sells is 207000$.

A down payment is the initial amount a buyer pays to purchase an expensive product or service. The down payment represents a portion of the total purchase price, and the buyer often takes out a loan for the rest.

The formula loan calculators use is I = P * r *T in layman's terms Interest equals the principal amount multiplied by your interest rate times the amount in years.

M = S − D where M is the mortgage loan amount, S is the selling price, and D is the down payment.

M = $230,000 -  $23,000

and  =   207000$

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The required coordinates of B are (0, 6) for the given parabola.

The x-intercept is defined as an intercept that is located at the x-axis of the plane, is the location or coordinate from where the line crosses.

To determine the coordinates of B, we can use the information given in the problem.

A is an x-intercept, which means that the y-coordinate of A is 0, and it can be found by setting x = 0 in the equation for f(x).

The line AB is g(x) = 3x + 6. This line is a straight line and it is perpendicular to the x-axis at B, which means that the x-coordinate of B is 0.

Therefore, we can set x = 0 in both equations to find the y-coordinate of B.

For f(x), we have:

f(0) = a × 0² + b × 0 + c = c

For g(x), we have:

g(0) = 3 × 0 + 6 = 6

Since the line AB passes through the turning point B, we know that the y-coordinate of B is equal to both f(0) and g(0). Therefore, we have:

c = 6

So, the coordinates of B are (0, 6).

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Answer:

x=7/6

Step-by-step explanation:

add 2/3 to both sides

a) "What is your age?" is a quantitative data.

b) "Are you male or female?" is a categorical data.

c) "When did you first start reading the wsj?" is a categorical data.

d) "How long have you been in your present job or position?" is a quantitative data.

e) "What type of vehicle are you considering for your next purchase?" is a categorical data.

(a) "What is your age?" - This question provides quantitative data because age is a numerical value that can be measured and ordered in a meaningful way. Respondents could give an answer such as "25", "45", or "70", for example, which can be used to calculate statistics such as the mean or median age of the survey population.

(b) "Are you male or female?" - This question provides categorical data because the responses fall into discrete, non-numeric categories (in this case, "male" or "female"). It's not possible to order the responses in a meaningful way, since there is no inherent numerical value associated with being male or female.

(c) "When did you first start reading the WSJ?" - This question provides categorical data because the possible responses fall into discrete, non-numeric categories (high school, college, early career, mid career, late career, or retirement). While it's possible to order the categories in a logical sequence, they don't represent numerical values.

(d) "How long have you been in your present job or position?" - This question provides quantitative data because the responses can be measured as numerical values (for example, "3 years", "10 years", or "25 years"). The data can be used to calculate statistics such as the average length of time that respondents have been in their current position.

(e) "What type of vehicle are you considering for your next purchase?" - This question provides categorical data because the possible responses fall into discrete, non-numeric categories (sedan, sports car, SUV, minivan, etc.). While it's possible to order the categories in a logical sequence based on size, price, or other factors.

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The weighted average grade of the student is 85.6% calculated by multiplying the weight of each category with the average score of that category, and summing up the results.

To find the weighted average grade of the student, we can use the following formula:

Weighted average = (weight of category 1 x average of category 1) + (weight of category 2 x average of category 2) + ... + (weight of category n x average of category n)

where n is the number of categories being considered.

Using this formula and the information given in the question, we can calculate the weighted average as follows:

Weighted average = (0.30 x 85%) + (0.40 x 83%) + (0.20 x 89%) + (0.10 x 91%)

= 25.5% + 33.2% + 17.8% + 9.1%

= 85.6%

Therefore,

The weighted average grade of the student is 85.6%.

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ANSWER is one- incher=1 while two inch binder=2.By using simultaneous equation.

For the given inequality, the values of u are:

We want to see which ones of the values are solutions of the inequality:

u ≤ 10

So u can be smaller than 10, or equal to 10.

For example, for the irst case u = 8.

8  ≤ 10

This is true, because 8 is smaller than 10.

Then:

u = 8 is a solution.

u = 4 is a solution.

u = 10 is a solution.

u = 13 is not a solution.

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The number of tots Rew has = X and X∈[0,5] or X(10,∝).

What is a number line?

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

Let the number of tots Rew has = X.

It is given that Rew has either no more than 5 tots or more than 10 tots.

This means that the number of tots is either less than 5 or greater than 10.

which mean that X≤5 or X>10.

X∈[0,5] or X(10,∝)

The graph of the number line is attached below.

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