The classic tradeoff between "guns and butter" states that when a society spends more on national defense, it has less to spend on consumer goods to raise the standard of living.
a. True
b. False

The number of months before the cost is the same as Plan A is 25 months.

The linear equation that represents the cost of plan A = cost per month x number of months

$70 x m = $70m

The linear equation that represents the cost of plan B = (cost per month x number of months) + cost of the phone

($50 x m) + $500

= $50m + $500

When the costs are the same, the two equations would be equal

$70m = $50m + $500

Solve for m:

Combine similar terms: $70m - $50m = $500

Add similar terms: $20m = $500

Divide both sides of the equation by 20 = 500 / 20

m = 25 months

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Since dy/dx > 0 for x = -7 and dy/dx < 0 for x = -9 , So this is a turning point.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and

constants.

So, the given expression ,

y = 2x^2 + 32x -4

So, first we have to find the derivative dy/dx

and than solve for dy/dx = 0

The derivative of any term x^n is equals to n*x^n-1 so for this polynomial

2x^2 + 32x - 4

The derivative could be

2.2x+1.32+0.-4

dy/dx = 4x+32

To calculate the turning points

let this equals to 0.

4x+32 = 0

x = -32/4

x = -5

By substituting this into the original equation, the turning point is at (-8,-137).

Therefore, Since dy/dx > 0 for x = -7 and dy/dx < 0 for x = -9 , So this is a turning point.

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The area of the large pizza is approximately equal to 112.984 square inches.

Herein we need to determine the area occupied by a large pizza (A), in square inches, and based on given input by circumference of a small pizza (s), in inches. Then, we need the following formulas:

Circumference

s = π · D

Area

A = 0.25π · D²

Where D is the diameter, inches.

First, determine the diameter of the small pizza:

D = s / π

D = 12.56 / π

D ≈ 3.998 in

Second, calculate the diameter of the large pizza:

D' = 3 · (3.998 in)

D' = 11.994 in

Third, obtain the area of the large pizza:

A = 0.25π · (11.994 in)²

A ≈ 112.984 in²

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(a) List of variables is Years, Country, Arms control and disarmament, colonialism, economic development, human rights, nuclear weapons, and materials, and Palestinian conflict.

(b) Each variable is numeric if the variable assumes number values and it will be categorical if it assumes labels.

(a) The list of variables is:

The variables that can be used in this visualization can be Years, Country, Percentage that said yes, Arms control and disarmament, colonialism, economic development, human rights, nuclear weapons, and materials, and Palestinian conflict.

(b) Category of different variables:

Years: Numerical and discrete

years are number values but the voting has not been done in the same interval so it is a numerical and discrete variable.

Country: Categorical and not ordinal

country name assumes as labels hence it is a categorical variable.

The percentage that said yes: Numerical and continuous

The percentage indicates number values so it is a numerical value.

And following is also assumed as a label so these are also categorical values:

Arms control and disarmament: categorical and not ordinal

colonialism: categorical and not ordinal

economic development: categorical and ordinal

human rights: categorical and ordinal

Nuclear weapons and materials: categorical and not ordinal.

Palestinian conflict: Categorical and not ordinal

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The complete question is:

the visualization below shows voting patterns in the united states, Canada, and Mexico in the united nations general assembly on a variety of issues. specifically, for a given year between 1946 and 2015, it displays the percentage of roll calls in which the country voted yes for each issue. this visualization was constructed based on a dataset where each observation is a country/year pair.

1) List the variables used to create this visualization.

2) Indicate wheater each variable in the study is numerical or categorical. If numerical, identify as continuous or discrete. If categorical, identify as the variable is ordinal.

This suggests that the data set has a skewed distribution with a long tail of larger values.

This suggests that the data set has a skewed distribution, meaning that the data is not evenly distributed. The mean being much larger than the median indicates that there are a few larger values in the data set that are pulling the mean up and creating a long tail of larger values.  This makes the distribution look lopsided, with a majority of the values being clustered around the median, and a few larger values that are skewing the mean higher.

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Therefore , the solution of the given problem of percentage comes out to be a value is 55.

In mathematics, a percentage is a number any figure that is stated as a proportion of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. The "%" symbol, however, is frequently used to denote it. The % amount has no dimensions and is flat. Because the numerator of percentages is 100, they are effectively fractions. To show that a number is a percentage, the percent sign (%) should be put in front of it. On a test, for instance, you would receive a 75% if you gave the answer 75 out of the total questions.

Here,

Given :

=> 20 /100 * a =11

=> a  = 11 *100 /20

=> a  = 1100 /20

=> a = 55

Thus , a is 55 .

Therefore , the solution of the given problem of percentage comes out to be a value is 55.

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If due to gravity, an object falls 16t^2 feet in t seconds. You drop a rock from a bridge that is 75 feet above the water. The rock will hit the water in 2 seconds?

Given data:

Object falls = 16t² feet in t seconds

Rock from a bridge = 75 feet above the water

So,

72 =16t²

t² = 72/16

t²=  4.5

t = √4.5

t  =  2.12 seconds to hit the water

Therefore we can conclude that the rock will hit the water in 2 seconds.

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The standard deviation of the total weight of the boxes that are shipped from this source is 3.02 pounds.

The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Given:

Case A:

Standard Deviation= 0.3 pounds

mean weight= 1.5 pounds

Case B:

Standard Deviation= 0.1 pounds

mean weight= 0.5 pounds

Case C:

Standard Deviation= 3 pounds

mean weight= 12 pounds

let A is the Weight of boxes, B is the weight of packing and C is the weight of boxes.

ver(total)= ver A + ver B + ver C

Below is the Formula used:

SD = √variance

So, ver (total) = 0.3² + 0.1²+ 3²

ver (total) = 9.1 SD

ver (total) =√9.1

ver (total) = 3.02

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The complete Question is:

Suppose that the mean weight of the boxes is 1.5 pounds with a standard deviation of 0.3 pound, the mean weight of the packing material is 0.5 pound with a standard deviation of 0.1 pound, and the mean weight of the books shipped is 12 pounds with a standard deviation of 3 pounds. Assuming that the weights are independent, what is the standard deviation of the total weight of the boxes that are shipped from this source?

Answer:

all

Step-by-step explanation:

all of them

The statements that are true regarding the areas are that each palette icon will always allow you to drag only one fill area onto the graph. Changing the position of the other objects on the graph may change the shape of the possible regions you may fill.

The statement "Each palette icon will always allow you to drag only one fill area onto the graph." is true.

The statement "Areas can be used to shade a region of any shade." is false. Areas can be used to shade a region in a specific colour or pattern, but not necessarily any shade.

The statement "Changing the position of the other objects on the graph may change the shape of the possible regions you may fill." is true.

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answer: In this case, -0.50, -0.10, 0.60, 0.68, 0.98 are all correlation coefficients and -0.50 is the least and 0.98 is the greatest among the given correlation coefficients.

but why? The correlation coefficients can be ordered from least to greatest as:

-0.50, -0.10, 0.60, 0.68, 0.98

A correlation coefficient is a measure of the strength and direction of a linear relationship between two variables. The value of the coefficient ranges from -1 to 1, where:

A coefficient of -1 represents a perfect negative correlation, meaning that as one variable increases, the other variable decreases.

A coefficient of 0 represents no correlation, meaning that there is no linear relationship between the two variables.

A coefficient of 1 represents a perfect positive correlation, meaning that as one variable increases, the other variable also increases.

We need to calculate the area bounded by the given arcs . As we know that if [tex]\theta[/tex] is the angle subtended at the centre by the arc , then ; the area is given by ,

[tex]\longrightarrow Area =\dfrac{\theta}{360^o}\times \pi r^2 \\[/tex]

And here ,

Therefore on substituting the respective values, we have;

[tex]\longrightarrow Area =\dfrac{120^o}{360^o}\times \pi (6m)^2 \\[/tex]

Simplify,

[tex]\longrightarrow Area =\dfrac{1}{3}\times 3.14 \times 36m^2 \\[/tex]

[tex]\longrightarrow \underline{\underline{ Area = 37.68 \ m^2}} \\[/tex]

And we are done!

Answer:

The number is 7

Step-by-step explanation:

1. Create the equation needed to solve this

Lets think of a number as x. We have a number multiplied by 6 and have 4 added to it.

We get:

6x + 4

Now this sum is equal to the product of 2 and 23. We connect this to get

6x + 4 = 2(23)

We can simplify this to

6x + 4 = 46

2. Solve for x

6x + 4 = 46

Subtract 4 from both sides

6x = 42

Divide both sides by 6

x = 7

Therefore the number is 7

The first plane is farther from the airstrip after the second leg

The first plane

Initial distance = 150 miles west

Additional distance = 220 miles 30 degrees SW

This means that

Additional distance = 220 * cos(30) miles SW

Additional distance = 190.53 miles

Total distance = 150 + 190.53 = 340.53

The second plane

Initial distance = 220 miles east

Additional distance = 150 miles x degrees SE

This means that

Additional distance = 150 * cos(x) miles SW

Total distance = 220 + 150 cos(x)

Given that

x < 30

We have

Second plane < First plane

220 + 150 cos(x) < 340.53

Evaluate

cos(x) < 0.8035

Take the arc cos of both sides

x < 36

x < 36 is not the same as x < 30

Hence, the first plane is farther

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a. The initial quantity of radioactive material is 0.68 g.

b. It will take an additional 7.15 years for the amount of radioactive material to reduce to 0.2 g.

a. In order to find the initial quality of radioactive material, we will use the formula:

Initial Quality = Final Quantity * (1 - Reduction Rate)^Years

We know that -

the final Quantity is 1.52 g, the reduction rate is 18% (or 0.18), and the number of years is 4.

Initial Quantity = 1.52 g * [tex](1 - 0.18)^4[/tex]

Initial Quantity = 1.52 g * 0.452

Initial Quantity = 0.68 g

Hence, the initial quantity of the radioactive material is 0.68 g.

b. In order to find how many more years it will take for the amount of radioactive material to reduce to 0.2 g, we will use the formula:

Years = log(Final Quality / Initial Quality) / log(1 - Reduction Rate)

We know that -

the final quality is 0.2 g, the initial quality is 0.68 g, and the reduction rate is 18% (or 0.18).

Years = log(0.2 / 0.0.68) / log(1 - 0.18)

Years = 7.15

Therefore, it will take an additional 7.15 years for the amount of radioactive material to reduce to 0.2 g.

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Answer: We can use trigonometry to solve this problem.

Let x be the length of the ladder, and h be the height of the ladder.

We can use the tangent function to relate the angle of elevation, the length of the ladder, and the height of the ladder:

tan(74°) = h / x

We know that x = 12 ft and we can find h.

We can cross multiply and solve for h:

x * tan(74°) = h

12 * tan(74°) = h

We can use a calculator to find the value of h, this will give us the height of the ladder.

Finally, we can use the Pythagorean theorem to find the length of the ladder:

x^2 = h^2 + 12^2

x = √(h^2 + 12^2)

Round your answer to the nearest tenth, we have x = √(h^2 + 12^2)

We can use the value of h to find the length of the ladder.

However, without the value of h it is not possible to find the length of the ladder.

Step-by-step explanation:

A graph is a visual representation of data or information using points, lines, or bars.

How to plot the Graph?

To plot a graph, you need to have a set of x and y values that correspond to points on the graph. Once you have the data, you can use a tool such as a graphing calculator, spreadsheet software or specialized graphing software to plot the points and create the graph.

This sequence appears to be a geometric sequence. In a geometric sequence, the ratio between any two consecutive terms is always the same. In this case, the ratio between consecutive terms decreases by a factor of 1/4 each time.

The first five terms of the sequence are: (64,1), (16,2), (4,3), (2,4), (0,5)

A recursive definition of the sequence is a definition that expresses each term of the sequence in terms of one or more of the previous terms.

This definition says that each term of the sequence is the previous term divided by 4.

It's important to note that the graph you provided does not have a clear representation of the sequence, the points (64,1) (16,2) (4,3) (2,4) (0,5) does not represent a sequence as the x-coordinate does not represent the nth term of the sequence. The graph does not provide enough information to determine if it's arithmetic or geometric, or to list the first five terms of the sequence, or to write a recursive definition of the sequence.

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Step-by-step explanation:

83 in burn in 5 hours.

so, we have a 83/5 speed ratio.

directly proportional means

y = kx

with k being constant for all values of x.

83 = k×5 = 5k

k = 83/5

15 in burn in x hours.

therefore,

15 = 83/5 × x

75 = 83x

x = 75/83 hours

this can be also calculated like this :

because of the direct proportionality, 15/x must have the same ratio as the original 83/5.

83/5 = 15/x

83x/5 = 15

83x = 75

x = 75/83 hours = 0.903614458... hours

Answer:

Step-by-step explanation:

The value of x that satisfies the equation 5^x = 140.50 is given as follows:

x = 3.07.

The exponential equation for this problem is defined as follows:

5^x = 140.50.

We want to isolate the variable x, hence we have to apply the inverse operation to the base of 5 elevated to x, which is the logarithm of base 5.

Hence the solution for x is obtained as follows:

log5(5^x) = log5(140.50)

x = log(140.50)/log(5) -> change of base of logarithms.

x = 3.07.

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The  the length and width of the rectangular field are respectively; 15 yards and 11 yards

The perimeter of a rectangle is given by the formula;

Perimeter = 2(Length + width)

We are given;

Perimeter = 52 yards

Length(L) = W + 4

Width = W

Thus;

2(W + W + 4) = 52

2W + 4 = 52/2

2W + 4 = 26

2W = 22

W = 11 yards

L = 11 + 4

L = 15 yards

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The equivalent expression of the given expression is {4/y - 56}.

Given is the expression as -

8(1/2y - 7)​​

The given expression is -

8(1/2y - 7)​​

(8 x 1/2y - 8 x 7)

4/y - 56

Therefore, the equivalent expression of the given expression is {4/y - 56}.

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{Complete question is

Write an equivalent expression for 8(1/2y - 7)​​}

For 235 weeks the show lasts.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

for example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A television show aired once a week for 4.5 years.

So, In four years number of weeks are

= 52.1429 weeks

and, in 6 months the number of weeks

= 4.34524 weeks

So, the number weeks the show last

= 52.1429 x 4 + 4.34524 x 6

= 234.6431

= 235 weeks

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The number of students from given linear equation after 6 weeks will be 45.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

As given linear equation for students is

y=-2.5t + 60

where where t is the number of weeks her students have been taking

the class and y = no. of students.

To find students after 6 weeks put y=6

Therefore, y=-2.5*6+60

y=45

Hence,

         The number of students from given linear equation after 6 weeks will be 45.

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Right question:-

Alexis is working with her English classes to make sure they are

all able to pass the upcoming state exam. From last year's data,

she predicts the number of students that will not pass the exam

is modeled by the linear equation:

y=-2.5t + 60,

where t is the number of weeks her students have been taking

the class and y = no. of students.

Find mo. of students after 6 weeks.

The value obtained when we subtract the given fractions is 21/8 and the 20% of 32.5 gives the amount $6.50.

We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

Given the following expression:

4 (1/2) - 1 (7/8)

Convert the mixed fractions into simple fractions:

9/2 -15/8

Take the LCM of the denominator:

36/ 8 - 15/8

21/8

2. 20% of x = 6.50

20/100 (x) = 6.50

20x = 650

x = 650/20

x = 32.5

Hence, the value obtained when we subtract the given fractions is 21/8 and the 20% of 32.5 gives the amount $6.50.

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The classification of the angles are;

a) ∠3 and ∠5; Alternate Angles

b) ∠1, ∠2 and ∠3; three interior angles of a triangle.

c) ∠2 and ∠3; Complementary angles

d) ∠4 and ∠5; Supplementary angles

We know that the sum of angles in a triangle is 180 degrees and as such it means that ∠1, ∠2 and ∠3 are classified as three interior angles of a triangle.

We know that alternate angles are defined as angles that occur on opposite sides of the transversal line and have the same size. Thus;

∠3 and ∠5 are alternate angles.

Since ∠1 is 90 degrees, then it means that ∠2 and ∠3 are complementary angles.

Similarly, ∠4 and ∠5 are called supplementary angles because they sum up to 180 degrees.

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From the given options, option B is the only statement that is not true is ∠C ≅ ∠E for congruent

What is the congruence theorem?

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

If Δ ABC is congruent to Δ DEF, then its corresponding parts must be congruent.

segment AB ≅ segment DE

segment BC ≅ segment EF

segment AC ≅ segment DF

∠A ≅ ∠D

∠B ≅ ∠E

∠C ≅ ∠F

Therefore, from the given options, option B is the only statement that is not true is ∠C ≅ ∠E.

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"Your question is incomplete, probably the complete question/missing part is:"

If triangle ABC is congruent to triangle DEF, which statement is not true?

A) Segment AB ≅ segment DE

B) ∠C ≅ ∠E

C) Segment BC ≅ segment EF

D) ∠A ≅ ∠D

From the given options, option B is the only statement - 1

Number of integers 'p' for which there exist a triangle with the given side length 3p -1 , 3p , p² + 1 is equal to five that is 1, 2, 3, 4, 5.

Using triangular inequality of triangle :

sum of two sides > third side

a. 3p - 1 + p² + 1 > 3p

⇒p² > 0

True result.

b. 3p + p² + 1 > 3p - 1

⇒ p² > -2

True result.

c. 3p - 1 + 3p > p² + 1

⇒ p² -6p + 2 < 0

Roots are : p = [ -(-6) ± √(-6)² -4(1)(2) ] /2(1)

                     = ( 6 ± √28 ) 2

                     = 5.6 or 0.35

Integer value of p are in between 0.35 to 5.6 are :

1, 2, 3, 4, 5

Therefore, the integer value of 'p' for the given side length of the triangle is equal to five that is 1, 2, 3, 4, 5.

For how many positive integers 'p' does there exist a triangle with sides of length 3p-1 , 3p , and p² + 1 ?

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The rate of change of the angle of elevation is approximately - 2.597 degrees per second (-0.045 radians per second). (Correct choice: C)

In this problem we find the case of a drone that travels horizontally, at constant height (h), in meters. The rate of change of the angle of elevation (θ'), in degrees per second, can be found from trigonometric functions and derivatives:

tan θ = y / x

Where:

By derivatives:

sec² θ · θ' = - y · x⁻² · x'

θ' = - (y · x⁻² · x') / sec² θ

Where x' is the speed of the drone, in meters per second.

If we know that y = 5 m, θ = π / 6 and x' = 5 m / s, then the rate of change of the angle of elevation is:

x = y / tan θ

x = (5 m) / tan (π / 6)

x ≈ 2.887 m

θ' = - [(5 m) · (2.887 m)⁻² · (5 m / s)] / sec² (π / 6)

θ' ≈ - 2.597 degrees per second (- 0.045 radians per second)

Note - Please notice that negative sign indicates that angle is decreasing.

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