in the US, 1 in 16 (6.25%) will be diagnosed with lung cancer in their lifetime.

(A) in a random sample of 100 americans what is the probability that less than 5% will be diagnosed with lung cancer?

(B) suppose that a random sample of 100 americans who smoke cigarettes results in 20 or more being diagnosed with lung cancer. what might you conclude ( is 20 or more normal and if it's rare, what do you think this means)?

Answer:

Step-by-step explanation:

y = 3x + 9

The experimental probability that the next train to arrive at Danville Station will be on time is 3/4 or 0.75.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The experimental probability of the next train to arrive at Danville Station being on time is given by the number of on-time trains divided by the total number of trains that arrived -

experimental probability = number of on-time trains / total number of trains

From the information given, we know that out of the last 20 trains to arrive, 15 were on time. Therefore -

number of on-time trains = 15

total number of trains = 20

Substituting these values into the equation, we get -

experimental probability = 15 / 20

Simplifying the fraction, we get -

experimental probability = 3/4

Therefore, the experimental probability value is obtained to be 3/4 or 0.75.

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The Converse of the Pythagorean Theorem is proved below.

What is Pythagoras Theorem ?

Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The converse of the Pythagorean theorem states that if a triangle has sides of length a, b, and c, where c is the longest side, and a² + b² = c², then the triangle is a right triangle.

To prove the converse of the Pythagorean theorem, we can use the fact that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. That is, if a triangle has sides of length a, b, and c, where c is the longest side and c² = a² + b², then the triangle is a right triangle.

Proof:

Suppose we have a triangle ABC, with sides of length a, b, and c, where c is the longest side. Assume that a² + b² = c². We want to show that triangle ABC is a right triangle.

We will use the Law of Cosines to show that angle C is a right angle. The Law of Cosines states that for any triangle ABC with sides of length a, b, and c opposite angles A, B, and C, respectively:

c² = a² + b² - 2ab cos(C)

Substituting a² + b² = c² into this equation, we get:

c² = c² - 2ab cos(C)

2ab cos(C) = 0

cos(C) = 0

Since 0 is the cosine of 90 degrees, this implies that angle C is a right angle. Therefore, triangle ABC is a right triangle.

Thus, this completes the proof of the converse of the Pythagorean theorem.

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the organization needs to sell at least 22 tickets to break even.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

Let C be the total production cost and n be the number of tickets sold.

From the problem, we know that the organization had a net loss of $800 after selling 10 tickets, so we have:

10(70) - C = -800

Simplifying, we get:

C = 1500

This means that the total production cost was $1500.

The revenue from selling n tickets at $70 per ticket is given by:

R = 70n

Substituting the values of R and C, we get:

70n = 1500

Solving for n, we get:

n = 1500/70 = 21.43

Since we can't sell a fraction of a ticket, we need to round up to the nearest whole number.

Therefore, the organization needs to sell at least 22 tickets to break even.

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The coordinates of the point P on the directed line segment from A to B such that P is 2/3 the length of the line segment from A to B are (-1, 2).

The coordinates of point P are obtained applying the proportions in the context of the problem.

P is 2/3 the length of the line segment from A to B, hence the equation is given as follows:

P - A = 2/3(B - A)

Then the x-coordinate of P is obtained considering the x-coordinates of A and B as follows:

x - 9 = 2/3(-6 - 9)

x - 9 = -10

x = -1.

The y-coordinate of P is obtained considering the y-coordinates of A and B as follows:

y + 8 = 2/3(7 + 8)

y + 8 = 10

y = 2.

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1. {0, 1, 3, 4, 6}; 2. {4, 6}.

Step-by-step explanation:

1. А={0, 1, 2, 3}, B={2, 4, 5, 6}, C={2, 5, 7, 9}; (A∪B)-(B∩C)-?

a) A∪B⇔{0, 1, 2, 3, 4, 5, 6};

b) B∩C⇔{2, 5};

c) (A∪B)-(B∩C)⇒{0, 1, 3, 4, 6}.

2. A={4, 6, 8, 10}, B={4, 6, 8}, C={1, 2, 3, 4, 7}, D={3, 5, 6, 7}; A∩(D∪(B∩C))=?

a) B∩C⇔{4};

b) D∪(B∩C)⇔{3, 4, 5, 6, 7};

c) A∩(D∪(B∩C))⇒{4, 6}.

Around [tex]312.57[/tex] yards are required to complete a full lap of the circuit.

The entire movement of an item, independent of direction, is called distance. Regardless of an object's beginning or finishing position, distance may be defined as the amount of ground it has travelled.

As a result, distance is indeed a scalar quantity. The whole path an item has taken can be used to define the distance from it. Think about it this way. If a car drives 5 km east, then turns to head north for 8 km, the final distance driven by the automobile must be 13 km.

The circumference of a semicircle with diameter d is [tex](pi/2)d[/tex]. Therefore, the length of each semicircular section is [tex](pi/2) * 36 = 18pi[/tex].

The total distance around the track is the sum of the lengths of the two straight sections and the two semicircular sections.

Distance around track [tex]= 2(100 yards) + 2(18pi yards)[/tex]

[tex]= 200 yards + 36pi yards[/tex]

[tex]= 312.57 yards[/tex] (rounded to two decimal places)

Therefore, the distance around the entire track is approximately [tex]312.57[/tex]yards.

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Answer:assuming its a rectangle its 13.5

Step-by-step explanation: L x H = Area

Answer:

Step-by-step explanation:

To find the total distance traveled in the first second, we need to find the distance traveled during the first half-second and then double it.

The particle starts 2 cm to the right of 0, so its position function is given by:

s(t) = t - t^2 + 2

The distance traveled by the particle during the first half-second (from t = 0 to t = 0.5) is given by:

distance = |s(0.5) - s(0)|

We have:

s(0.5) = 0.5 - (0.5)^2 + 2 = 2.25 cm

s(0) = 0 - 0^2 + 2 = 2 cm

So, the distance traveled during the first half-second is:

|2.25 - 2| = 0.25 cm

To find the total distance traveled in the first second, we double this distance:

total distance = 2 * 0.25 = 0.5 cm

Therefore, the total distance traveled in the first second is 0.5 cm.

Therefore , the solution of the given problem of equation comes out to be  f(x) = sin(/2 x) (when x = 1 or 2).

Variable words are commonly used in complex algorithms to show consistency between two statements that are not compatible. Academic expressions called equations are used to show the equality of various academic numbers. In this case, normalization yields b + 7 as opposed to a single formula the fact that split 12 into two parts, which can be used with data collected from y + 7.

Here,

The goal is to construct a trigonometric equation with only answers at

x = 1 and x = 2.

f(x) = A sin(Bx+C+D)

=> B + C + D + A = 0 (equation 1)

=> Equation 2: A sin(2B + C + D) = 0

=> B + C sin A = 0 (equation 3)

=> Sin(2B+C) = A = 0 (equation 4)

Since sin(x) = 0 when x is a multiple of, formulae 3 and 4 can be rewritten as follows:

=> B + C = nπ (equation 5)

=> 2B + C = mπ (equation 6)

with numbers n and m. When we simultaneously solve equations 5 and 6 for B and C, we obtain:

=> B = (m - n)π/2 (equation 7)

=> C = nπ - B (equation 8)

=> When x = 1, C = /2 - /2 = 0.

=> When x = 2, C =  − /2 = 3/2.

Thus, the result is as follows:

when f(x) = sin(/2 x) (when x = 1 or 2)

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Answer:

It will be same as angle x because they are on the same line and are alternative angles

So, measurement of angle u will be u=152

Step-by-step explanation:

Hope this helps:)

Good luck

Given:-

To find:-

Answer:-

Here since the given triangle is a right angled triangle, we may use the trigonometric ratios . We can see that perpendicular and base are involved in this question whose measures are "x" and "√10" respectively with respect to 60° angle. So here we may use the ratio of tangent as , in any right angled triangle,

[tex]\implies\tan\theta =\dfrac{p}{b} \\[/tex]

and here p = x , and b = √10 . So on substituting the respective values, we have;

[tex]\implies \tan\theta = \dfrac{x}{\sqrt{10}} \\[/tex]

Also the angle here is 60° , so that;

[tex]\implies\tan60^o =\dfrac{x}{\sqrt10} \\[/tex]

The value tan60° is √3 , so we have;

[tex]\implies \sqrt3 =\dfrac{x}{\sqrt10}\\[/tex]

[tex]\implies x =\sqrt{10}\cdot \sqrt{3}\\[/tex]

[tex]\implies x =\sqrt{10\cdot 3} \\[/tex]

[tex]\implies x =\sqrt{30} \\[/tex]

The value of √30 is approximately 5.48 , so that;

[tex]\implies \underline{\underline{\red{\quad x = 5.48\quad }}} \\[/tex]

Therefore the value of x is approximately 5.48 .

Answer:

The length of side x in simplest radical form is [tex]\sqrt{30}[/tex].

Step-by-step explanation:

From inspection of the given right triangle, we can see that the interior angles are 30°, 60° and 90°. Therefore, this triangle is a 30-60-90 triangle.

A 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio  1 : √3 : 2.  Therefore, the formula for the ratio of the sides is b: b√3 : 2b where:

We have been given the side opposite the 30° angle, so:

[tex]\implies b=\sqrt{10}[/tex]

The side labelled "x" is the side opposite the 60° angle, so:

[tex]\implies x=b\sqrt{3}[/tex]

Substitute the found value of b into the equation for x:

[tex]\implies x=\sqrt{10}\sqrt{3}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}[/tex]

[tex]\implies x=\sqrt{10 \cdot3}[/tex]

[tex]\implies x=\sqrt{30}[/tex]

Therefore, the length of side x in simplest radical form is [tex]\sqrt{30}[/tex].

[tex]\hrulefill[/tex]

We can also calculate the length of side x using the tangent trigonometric ratio:

[tex]\boxed{\tan \theta=\sf \dfrac{O}{A}}[/tex]

where:

From inspection of the given right triangle:

Substitute these values into the formula:

[tex]\implies \tan 30^{\circ}=\dfrac{\sqrt{10}}{x}[/tex]

[tex]\implies \dfrac{\sqrt{3}}{3}=\dfrac{\sqrt{10}}{x}[/tex]

[tex]\implies x\sqrt{3}=3\sqrt{10}[/tex]

[tex]\implies x=\dfrac{3\sqrt{10}}{\sqrt{3}}[/tex]

Rationalise the denominator by multiplying the numerator and denominator by √3:

[tex]\implies x=\dfrac{3\sqrt{10}}{\sqrt{3}}\cdot \dfrac{\sqrt{3}}{\sqrt{3}}[/tex]

[tex]\implies x=\dfrac{3\sqrt{10}\sqrt{3}}{3}[/tex]

[tex]\implies x=\sqrt{10}\sqrt{3}[/tex]

[tex]\implies x=\sqrt{10\cdot3}[/tex]

[tex]\implies x=\sqrt{30}[/tex]

Therefore, the length of side x in simplest radical form is [tex]\sqrt{30}[/tex].

The values of the side w and the angle x are 2.649 and 26. 206 degrees respectively.

It is important to note that there are different types of trigonometric identities are;

From the image shown, we have;

Using the sine identity

sin θ = opposite/hypotenuse

sin 32 = w/5

find the value

w = 2. 649

To determine the value of angle x , we have;

Using the sine identity

sin x = w/6

sin x = 2. 649/6

sin x= 0. 4416

Take the sine inverse

x = 26. 206 degrees

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Answer:313:)

Step-by-step explanation:

The quadratic equation on the graph can be written as:

y = x² + 6x + 8

Remember that a quadratic equation whose vertex is (h,k) and the leading coefficient is a, can be written as:

y = a*(x - h)² + k

Here we can see that the vertex is at (-3, -1), replacing that we will get:

y = a*(x + 3)² - 1

Now we can also see that it passes through the point (-2, 0), replacing these values we will get:

0 = a*(-2 + 3)² - 1

0 = a - 1

1 = a

Then the quadratic is:

y  = (x + 3)² - 1

Expanding that we get:

y = x² + 6x + 9 - 1

y = x² + 6x + 8

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Answer:

volume = 290m

Step-by-step explanation:

box 1

[tex]vol= lwh\\=3*5*6\\=90m[/tex]

box 2

[tex]vol=lwh\\=8*5*5\\=200m[/tex]

total volume = 90+200 =290m

A total possible number of bonuses awarded is given as follows:

6 bonuses.

The total number of bonuses awarded is obtained applying the proportions in the context of the problem.

The total amount of bonuses is of $5,000, and at least one $500 bonus and at least one $1000 bonus were awarded, hence the remaining amount to be awarded is of:

5000 - (500 + 1000) = $3,500.

For an amount of $3,500, a possible division of the bonuses is given as follows:

Hence a possible number of bonuses is given as follows:

2 + 1 + 3 = 6 bonuses.

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We may conclude after answering the presented question that As a equation result, we have demonstrated that mt = mu when t | u.

Make a note of the definition of t | u. It denotes the existence of an integer k such that u = tk.

To get mt = m, substitute u = tk into mt = mu (tk).

Rewrite m(tk) as (mt)k using the associative property of multiplication.

To get mt = (mt)k, substitute (mt)k for m(tk) in the equation mt = mu.

Multiply both sides by mt. If mt is greater than zero, we obtain 1 = k. If mt is zero, we must also have mu = 0, hence the equation holds.

Since 1 Equals k, we get u = tk = t(1) = t.

We get mt = mt by substituting u = t into the original equation mt = mu.

As a result, we have demonstrated that mt = mu when t | u.

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The point on the graph that tells you the amount of sugar you'll use if you don't make any pies is (0, 0).

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

In order to have a proportional relationship, the variables representing the amount of sugar and time must have the same constant of proportionality:

Constant of proportionality, k = y/x

Constant of proportionality, k = 4/3

Constant of proportionality, k = 12.

Therefore, the required equation is given by:

y = kx

y = 4x/3

When x = 0, the value of y is given by:

y = 4(0)/3

y = 0 pies.

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Answer:

A fraction tells you how many parts of a whole there are. When we find a fraction of an amount, we are working out how much that 'part' is worth within the whole. You can see fractions of amounts all around us

Step-by-step explanation:

i may be wrong but I tried

The mode for the region A is 2.6.

What exactly is mode?

In statistics, the mode is the value that has highest frequency in a data set. It is one of the three measures of central tendency, along with the mean and median.

To find the mode of a data set, you simply identify the value that appears most often. If no value is repeated, the data set has no mode.

The mode is particularly useful when dealing with categorical data or data that can be easily grouped into categories, such as colors, types of fruit, or letter grades. In such cases, the mode can provide insight into which category is most common or prevalent.

Now,

As given Values for Region A are

2.3  2.5  2.6  2.6  2.6  2.7  2.7  2.8

Here 2.6 comes most times or frequency of 2.6 is highest of all.

Hence,

           The mode for the region A is 2.6.

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Answer:

Alright

Step-by-step explanation:

50/1.428

Multiply the numerator by the denominator to get 50000/1428

Set equation up in long division format

Divide 50000 by 1428 to get 3

Divide 7160 by 1428 to get 5

Divide 200 by 1428 to get 0

Divide 2000 by 1428 to get 1

Divide 5720 by 1428 to get 4

Divide 80 by 1428 to get 0

Divide 800 by 1428 to get 0

35.014

Answer: 6

Step-by-step explanation:

21 - 1 = 20

20 - 2 = 18

18 - 3 = 15

15 - 4 = 11

11 - 5 = 6

13

First, we divide to figure out how much Jane makes an hour

143 ÷ 11 = 13

Second, we multiply multiply by 13 until we get 169

13 × 13 = 169

So Jane will make 169 dollars in 13 hours

Answer:

13 Hours

Step-by-step explanation:

$143 ÷ 11hrs = $13/hr that Jane is paid, so to find how many hours she will need to work to make $169

$169 ÷ $13 = 13 hours

Answer:

Step-by-step explanation:

Ranking:

Compound the interest every month instead of every two months.

Increase the interest rate by 1%.

Let the account increase for one more year.

Increase the starting amount by $100.

Calculations:

If the interest is compounded monthly instead of every two months, the final value would be $1,357.36, which is an increase of $9.18 compared to the original value.

If the interest rate is increased to 6%, the final value would be $1,411.58, which is an increase of $63.40 compared to the original value.

If the account increases for one more year at the same interest rate, the final value would be $1,435.09, which is an increase of $86.91 compared to the original value.

If the starting amount is increased by $100, the final value would be $1,421.61, which is an increase of $73.43 compared to the original value.

Answer:

Step-by-step explanation:

Simplify the expressionApply the logarithm power identityApply the logarithm product identitySimplify the expression2Exponentiate both sides

log10(4x8)=2log10(48)=2

48=102

x=258=258√

Answer:

[tex]yeah \: 2 + 2 = 4[/tex]