Suppose that y varies directly with x, and y=4 when x=20. (a) Write a direct variation equation that relates and y Equation: (b) Find y when x=9. y=​

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:

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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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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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 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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The win percentage is 79%

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

Given;

Number of games won=52

Number of games lost=14

Now, total games played= 14+52=66

Percentage of games won;

=(games won/total games)x100

= 52x100/66

=78.78

Therefore, the win percent will be 79%

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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:

Step-by-step explanation:

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!

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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Answer:

parallel

Brief explanation:

Well parallel lines have the same slopes sooo

these two lines are parallel

hence the answer

study hard

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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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 standard deviation of the sampling distribution of the sample mean would be 5/√30, or 0.87.

In order to use the formula sigma x = sigma/ to calculate the standard deviation of the sampling distribution of the sample mean, all three conditions must be met. The first condition is that n must be greater than or equal to 30. This is because the larger the sample size, the more likely it is that the population's distribution is approximately normal. The second condition is that the population's distribution is approximately normal. This is because the Central Limit Theorem states that when the sample size is large enough (usually n ≥ 30) the sample means will have an approximately normal distribution. The third condition is that the sample size is less than 10% of the population size. This is because samples that are too large can lead to sample means that are not representative of the population.

To calculate the standard deviation of the sampling distribution of the sample mean, we can use the following formula:

σx = σ/√n

Where σ is the population standard deviation, and n is the sample size. For example, if the population standard deviation is 5, and the sample size is 30, then the standard deviation of the sampling distribution of the sample mean would be 5/√30, or 0.87.

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In the simplest rational exponent form of "square root of x times the fourth root of x" is [tex]x^{1/6}[/tex].

Exponentiation is one of the mathematics operation.

Let mᵃ, where m and a are the real numbers.

And m is multiplied by a time to itself.

So, a is the exponent of m.

Given:

We have a phrase:

Square root of x times the fourth root of x.

In numerator form:

(√x)[tex]\sqrt[1/4]{x}[/tex]

Simplifying,

(√x)[tex]\sqrt[1/4]{x}[/tex],

= [tex]x^{1/2} x^{1/4}[/tex]

= [tex]x^{1/2+1/4}[/tex]

= [tex]x^{1/6}[/tex]

Therefore, [tex]x^{1/6}[/tex]the required simple rational form.

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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.

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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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

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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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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The probability that both chosen students are women is 0.3025 and the probability that at least one of the two students is a woman is 0.8075.

a) Probability of both chosen students being women = P(W1 ∩ W2) = P(W1) * P(W2)

= 0.55 * 0.55 = 0.3025

b) Probability of atleast one of the two students being a woman = P(W1 ∪ W2)

= P(W1) + P(W2) - P(W1 ∩ W2)

= 0.55 + 0.55 - 0.3025 = 0.8075

Therefore, the probability that both chosen students are women is 0.3025 and the probability that at least one of the two students is a woman is 0.8075.

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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

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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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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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 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)​​}

(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.

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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Answer:

Step-by-step explanation:

Correct answers only explained
------------------------------------------------------------------
We have the original equation as
72x + 12y = 60
If we multiply by 10 we get

720x + 120y = 600
First option

---------------------------------------------------------------

We can rewrite the original equation 72x + 12y = 60 as follows
Carry 72x to the right:
12y = 60 - 72x

Divide by 12
y = 5 - 6x
Second option

---------------------------------------------------------------

Rewrite  72x + 12y = 60 as

12y + 72x = 60  (same thing)

Divide by 6:
2y + 12x = 10

Third option

---------------------------------------------------------------

Rewrite 72x + 12y = 60 as

72x = 60 - 12y

Divide by 72

x = 60/72 -12y/72

Reduce to lowest fraction
x = 5/6 - y/6
Fifth option
------------------------------------------------

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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